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Geometric Formula PROOF Integration problems

Area of a Triangle Formula Proof example question

Use Integration techniques in order to derive the formula for the Area of a Triangle, A, such that

where b is the base and h is the height.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



Area of a Trapezoid Formula Proof example problem

Use Integration to derive the formula for the Area of a Trapezoid, A, such that

where b1 and b2 are bases and h is the height.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



Area of a Circle Formula Proof example

Use Integration to derive the formula for the Area of a Circle, A, such that

where r is the radius.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



Area of a Circle Formula Proof example question

Use Double Integration to prove the formula for the Area of a Circle, A, such that

where r is the radius.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



Volume of a Sphere Formula Proof example problem

Use the Disk Integration method to derive the formula for the Volume of a Sphere, V, such that

where r is the radius.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



Volume of a Cone Formula Proof example

Use the Disk Integration method to prove the formula for the Volume of a Right Circular Cone, V, such that

where r is the radius and h is the height.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



Volume of a Torus Formula Proof example question

Use the Washer Integration method to derive the formula for the Volume of a Torus, V, such that

where r is the inner (minor) radius and R is the outer (major) radius.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



Volume of a Torus Formula Proof example problem

Use the Shell Integration method to prove the formula for the Volume of a Torus, V, such that

where r is the inner (minor) radius and R is the outer (major) radius.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



Surface Area of a Cone Formula Proof example

Use Integration to derive the formula for the Lateral Surface Area of a Right Circular Cone, SA, such that

where r is the radius and h is the height.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



 

Surface Area of a Right Circular Cone Formula Proof with Double Integration example problem

Use Double Integrals to derive the formula for the Lateral Surface Area of a Right Circular Cone, SA, where

where r is the radius and h is the height.

 

Solution to this Calculus Geometric Formula Proof practice problem is provided in the video below!



 

Surface Area of a Sphere Formula Proof example question

Use Integration to prove the formula for the Surface Area of a Sphere, SA, such that

where r is the radius.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



 

Volume of a Torus Formula Proof example

Use the Cylindrical Coordinates (Triple Integration) method to prove the formula for the Volume of a Torus, V, such that

where r is the inner (minor) radius and R is the outer (major) radius.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



Volume of a Sphere Formula Proof example question

Use the Spherical Coordinates (Triple Integration) method to derive the formula for the Volume of a Sphere, V, such that

where r is the radius.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



Volume of a Cone Formula Proof example problem

Use the Spherical Coordinates (Triple Integration) method to derive the formula for the Volume of a Right Circular Cone, V, such that

where r is the radius and h is the height.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



Volume of a Torus Formula Proof example

Use the Spherical Coordinates (Triple Integration) method to prove the formula for the Volume of a Torus, V, such that

where r is the inner (minor) radius and R is the outer (major) radius.

 

Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!



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!





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