# Calculus Examples

,

To find the volume of the solid, first define the area of each slice then integrate across the range. The area of each slice is the area of a circle with radius and .

where and

Apply the power rule and multiply exponents, .

Multiply by .

Split the single integral into multiple integrals.

By the Power Rule, the integral of with respect to is .

Combine and .

Since is constant with respect to , move out of the integral.

By the Power Rule, the integral of with respect to is .

Combine and .

Substitute and simplify.

Evaluate at and at .

Evaluate at and at .

One to any power is one.

Raising to any positive power yields .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Multiply by .

Add and .

One to any power is one.

Raising to any positive power yields .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Multiply by .

Add and .

To write as a fraction with a common denominator, multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Multiply by .

Subtract from .

Combine and .

Move to the left of .