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Surface Area Integration problems

Surface Area of a Solid Integration problem example

Find the Surface Area of a solid generated by revolving the curve

, from    to   , about the x-axis.

 

Solution to this calculus Surface Area of a Solid Integration practice problem is provided in the video below!



 

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!






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