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Fundamental Theorem of Calculus #1 problems

First Fundamental Theorem of Calculus example question

Use the First Fundamental Theorem of Calculus to find the Definite Integral of f(x) = x2 – 2x, from x = 0 to x = 2

 

Solution to this Calculus Definite Integral practice problem is given in the video below!



HARD First Fundamental Theorem of Calculus example problem

Find the value of the following Definite Integral

when 

 

Solution to this Calculus Definite Integral practice problem is given in the video below!



Mean Value Theorem Integration problems

Integration with Mean Value Theorem example question

Estimate the Definite Integral value of a function f(x) = 3cos(x2) from

to

by using the Integral Mean Value Theorem.

 

Solution to this Calculus Definite Integral practice problem is given in the video below!



Integration with Mean Value Theorem example problem

Find the value of c that concludes the Integral Mean Value Theorem for the function f(x) = 3x2 from x = 0 to x = 2.

 

Solution to this Calculus Definite Integral practice problem is given in the video below!



Riemann Sum Definite Integral problems

Riemann Sum Integration example question

Find the Definite Integral of a function f(x) = x2 – 3 from x = 1 to x = 3, by using the Riemann Sum.

 

Solution to this Calculus Riemann Sum Definite Integral practice problem is given in the video below!



SAT Math problems (complete Playlist)

Find practice problems from all

8 official SAT Math practice tests

in the video series below.

 


 


Powerful SAT Math eBook (see video below) will dramatically raise your SAT Math score. This eBook contains 570 practice questions and 12 real SAT Math practice tests – 1,266 Math problems in total! The package you get includes complete solutions for all 1,266 problems – in other words, this solution manual contains detailed explanations for all 1,266 problems!

Please visit our Youtube channel video to see some user comments (success stories) with this eBook.

Buy this eBook online here

Watch the detailed video about the eBook below 

GRE Math problems (complete Playlist)

Explore a variety of GRE Math examples and practice problems that will help you raise your actual exam score.

 


 

GED Math problems (complete Playlist)

Explore lots of examples and practice problems that will help you improve your GED Math score!

The video playlist below covers whole numbers and operations, number sense, decimal numbers and operations, word problems, fractions and operations, number relationships, statistics and data analysis, percents, algebra, measurement, geometry, and more.


ACT Math Tips, Tricks & Strategies (complete Playlist)

Find lots of ACT Math tips, tricks and strategies

explored in practice problems that will help you boost your actual score.

 


 


Powerful SAT Math eBook (see video below) will dramatically raise your SAT Math score. This eBook contains 570 practice questions and 12 real SAT Math practice tests – 1,266 Math problems in total! The package you get includes complete solutions for all 1,266 problems – in other words, this solution manual contains detailed explanations for all 1,266 problems!

Please visit our Youtube channel video to see some user comments (success stories) with this eBook.

Buy this eBook online here

Watch the detailed video about the eBook below 

Math Tricks (complete Playlist)

Explore a variety of math tricks explored with practice problems that will help you solve real-life examples.


Math Puzzles (complete Playlist)

Find lots of Math puzzles, examples and practice problems to brighten your pastime.


Theoretical & Math Proof problems (complete Playlist)

Explore a variety of Theoretical and Proof examples and practice problems applicable to Algebra, Geometry, Trigonometry, Precalculus, Calculus, and Discrete Math courses.


Sequences & Series problems (complete Playlist)

Lots of different Sequences & Series examples and practice problems applicable to your Calculus or Precalculus courses.


Infinite Series problems (complete Playlist)

Explore a wide range of Infinite Series examples and practice problems for your Calculus or Precalculus courses.


Infinite Sequences problems (complete Playlist)

Find a variety of Sequences examples and practice problems for your Calculus or Precalculus courses.


Improper Integrals problems (complete Playlist)

Explore detailed Improper Integral examples and practice problems that will help you improve in this Calculus topic.


Hard & Complex Integration problems (complete Playlist)

Find challenging Integral and Antiderivatives examples and practice problems that will help you sharpen your Calculus skills.


Integration by Partial Fractions problems (complete Playlist)

Explore a variety of Integral and Antiderivatives partial fraction decomposition examples and practice problems applicable to your Calculus classes.


Integration by Parts problems (complete Playlist)

Find a wide range of Integral and Antiderivatives by Parts examples and practice problems to improve your knowledge of Calculus.


Integration by Substitution problems (complete Playlist)

Find a variety of Integral and Antiderivative substitution examples and practice problems to improve your Calculus knowledge.


Probability & Statistics problems (complete Playlist)

Find many different Probability and Statistics examples and practice problems that may be useful in your Algebra, Geometry, Precalculus, or Calculus courses.


Integration & Antiderivatives problems (complete Playlist)

Find many different Integration examples and practice problems that will help you improve your knowledge of Calculus.

Specific topics (all clickable links) in this section are provided below:

All of these topics and more difficult examples (including application problems and multiple integrals) are also compiled in one single playlist given below.


Music Theory problems (complete Playlist)

Explore a variety of Music Theory examples and practice problems in this tutorial.


Trigonometry problems (complete Playlist)

Find comprehensive Trigonometry examples and practice problems found in your Calculus or Precalculus courses.


 

Hydrostatic Force & Work problems (complete Playlist)

Explore lots of Hydrostatic Force & Work examples and practice problems for your Calculus course.

Definite Integrals and Antiderivatives will be used to solve application problems found in Physics and Engineering.

Work examples include Pumping Liquids, Pulling a Spring, Pulling Objects with Cable or Rope, and more.


Linear Algebra problems (complete Playlist)

Find a variety of Linear Algebra examples and practice problems in this course.


Precalculus problems (complete Playlist)

Explore many different Precalculus examples and practice problems to help you improve in this course.

Topics include polynomials, exponents, radicals, logarithms, equations, functions, graphs, limits, derivatives, sequences, series, application problems, and more!


Related Rates problems (complete Playlist)

Find a variety of Related Rates examples and practice problems to help you improve your knowledge in this topic.


Optimization problems (complete Playlist)

Go over lots of Optimization examples and practice problems that will help you understand this topic.


Limits problems (complete Playlist)

Find comprehensive Limit examples and practice problems for your Calculus or Precalculus courses.


Implicit Differentiation problems (complete Playlist)

Explore a variety of Implicit Differentiation examples and practice problems for your Calculus or Precalculus classes.


Derivative & Differentiation problems (complete Playlist)

Find lots of Differentiation and Derivatives examples and practice problems for your Precalculus or Calculus courses.


Geometry problems (complete Playlist)

Explore a variety of Geometry examples and practice problems applicable to K-12, Precalculus or Calculus courses.



 

Discrete Mathematics & Combinatorics problems (complete Playlist)

Get help with many different examples and practice problems in Discrete Mathematics that are applicable to Probability, Electrical Engineering, Computer Science, and other courses.


Differential Equations problems (complete Playlist)

Explore a variety of examples and practice problems in the Differential Equations course in the video playlist below.


Chemistry problems (complete Playlist)

Explore a variety of examples and practice problems for your Chemistry course.


Calculus problems (complete Playlist)

Find a variety of Calculus examples and practice problems to help you improve in Calculus 1, Calculus 2, Calculus 3, and more courses.

Topics include limits, continuity, differentiation, integration, parametric equations, polar coordinates, sequences and series, application problems, and more!


Algebra problems (complete Playlist)

Find detailed examples and practice problems for your Pre-Algebra, Algebra 1, Algebra 2, and College Algebra courses.

Topics cover addition, subtraction, division, multiplication, polynomials, logarithms, linear equations, quadratic equations, rational equations, absolute value inequalities, absolute value equations, functions, word problems, trigonometry, and more!



Actuarial Exam problems (complete Playlist)

Find many different practice problems and examples to succeed on your upcoming Actuarial Science classes and exams.

Topics include Probability, Statistics, and more.


SOA Exam P CAS Exam 1 Expected Value Variance Standard Deviation probability problems

Multiple Moment Generating Functions MGF example question

A company insures homes in three cities, J, K and L. Since sufficient distance separates the cities, it is reasonable to assume that the losses occurring in these cities are independent. The moment generating functions for the loss distributions of the cities are

Let X represent the combined losses from the three cities. Calculate  .

 

Solution to this Society of Actuaries Exam P practice problem is given in the video below!



Expected Value & Probability Density Function PDF example problem

Let X be a continuous random variable with density function

 {    

\dpi{150} \large 0            \dpi{150} \large \textup{otherwise}

 

Calculate the expected value of X.

 

Solution to this Society of Actuaries Exam P practice problem is given in the video below!



Moment Generating Function MGF example

Let X1 , X2 , X3 be a random sample from a discrete distribution with probability function

  {   

Determine the moment generating function, M(t), of  .

 

Solution to this Society of Actuaries Exam P practice problem is given in the video below!



Expected Value & Probability Density Function PDF word problem

An insurance company’s monthly claims are modeled by a continuous, positive random variable X, whose probability density function is proportional to

Determine the company’s expected monthly claims.

 

Solution to this Society of Actuaries Exam P practice problem is given in the video below!



Percentiles & Probability Density Function PDF example question

An insurer’s annual weather related loss, X, is a random variable with density function

    {   

Calculate the difference between the 30th and 70th percentiles of X.

 

Solution to this Society of Actuaries Exam P practice problem is given in the video below!



Standard Deviation & Moment Generating Function MGF example problem

An actuary determines that the claim size for a certain class of accidents is a random variable, X, with a moment generating function

Determine the standard deviation of the claim size for this class of accidents.

 

Solution to this Society of Actuaries Exam P practice problem is given in the video below!



Standard Deviation Table example

A probability distribution of the claim sizes for an auto insurance policy is given in the table below:

Claim Size 20 30 40 50 60 70 80
Probability .15 .10 .06 .20 .10 .10 .30

What percentage of the claims are within one standard deviation of the mean claim size?

 

Solution to this Society of Actuaries Exam P practice problem is given in the video below!



Variance & Cumulative Distribution Function CDF example question

A random variable has the cumulative distribution function

    {   

   

   

 

Calculate the variance of X.

 

Solution to this Society of Actuaries Exam P practice problem is given in the video below!



Variance word problem

A recent study indicates that the annual cost of maintaining and repairing a car in a town to Ontario averages 200 with a variance of 260. If a tax of 20% is introduced on all items associated with the maintenance and repair of cars (i.e., everything is made 20% more expensive), what will be the variance of the annual cost of maintaining and repairing a car?

 

Solution to this Society of Actuaries Exam P practice problem is given in the video below!



Euler Formula Complex Roots of the Characteristic Equation problems

Complex Roots of the Characteristic Equation example question

In each of the given examples, use Euler’s formula to write the given expression in the form a + ib.

 

Solution to this Differential Equations practice problem is given in the video below!



Wronskian of Functions problems

Wronskian of Functions example question

Find the Wronskian of the given pair of functions:

 

Solution to this Differential Equations practice problem is given in the video below!



Second Order Differential Equations with Constant Coefficients problems

Differential Equation with Constant Coefficients example question

Find the general solution of the given differential equation

 

Solution to this Differential Equations practice problem is given in the video below!



Exact Differential Equations problems

EXACT Differential Equation example question

Solve the differential equation

by first showing that it is exact and then find the solution.

 

Solution to this Differential Equations practice problem is given in the video below!



First Order Differential Equation Modeling Tank problems

First Order Differential Equation Modeling Tank example question

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 gram per liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liter per minute, the well-stirred solution flowing out at the same rate. Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.

 

Solution to this Differential Equations practice problem is given in the video below!



Homogeneous Differential Equations problems

Homogeneous Differential Equation Equation example question

Solve the differential equation

by showing it is homogeneous and separable and then find the solution.

 

Solution to this Differential Equations practice problem is given in the video below!



Separable Differential Equations problems

Separable Differential Equations example question

Solve the differential equation

by showing it is separable and then use Integration to find the solution.

 

Solution to this Differential Equations practice problem is given in the video below!



Integrating Factor Differential Equations problems

Differential Equation Integrating Factor example question

Solve the differential equation

by using the Integrating Factor solution method.

 

Solution to this Differential Equations practice problem is given in the video below!



Piecewise Functions Continuity Differentiability Calculus problems

Calculus Piecewise Function Continuity example problem

Find the value of a that will make f(x) continuous everywhere:

   

 

Solution to this Calculus Function Continuity practice problem is given in the video below!



Calculus Piecewise Function Continuity DIFFERENTIABILITY example question

Find the value of constants a and b that will make f(x) continuous everywhere:

 

Solution to this Calculus Function Continuity Differentiability practice problem is given in the video below!



Removal of Discontinuity problems

Removal of Discontinuity example question

Determine whether the Function Discontinuity is removable in the following functions:

 

 

 

Solution to these Calculus Continuity practice problems is given in the video below!



Continuity Graphs problems Calculus problems

GRAPH of Function Continuity example question

A function f is continuous at x = a if

‚ÄĘ f(a) is defined

‚ÄĘ ¬†exists

‚ÄĘ ¬†= f(a)

 

Various Calculus Continuity Graphs practice problems are discussed in the video below!



GED Math problems – Order of Operations

GED Math Order of Operations example question

Find the value of the following expressions using Order of Operations and P.E.M.D.A.S. rules.

(4 + 9) ‚ÄĘ 5 =¬†

12  7 + 4 = 

 = 

 + 9 = 

8 ‚ÄĘ 3 + 6 ‚ÄĘ 4 =¬†

4(5 + 3)2 =

6 + 21 ÷ 3  52 = 

 

Solution to these GED Math practice problems is given in the video below!






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