# Calculus Examples

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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
Simplify the integrand.
Simplify each term.
Remove parentheses around .
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Remove parentheses.
Simplify and combine like terms.
Simplify each term.
Use the power rule to combine exponents.
Move .
Use the power rule to combine exponents.
Move .
Use the power rule to combine exponents.
Move .
Use the power rule to combine exponents.
Multiply by to get .
Subtract from to get .
Apply the distributive property.
Simplify.
Multiply by to get .
Multiply by to get .
Remove unnecessary parentheses.
Subtract from to get .
Since integration is linear, the integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
By the Power Rule, the integral of with respect to is .
Combine fractions.
Write as a fraction with denominator .
Multiply and to get .
Since is constant with respect to , the integral of with respect to is .
By the Power Rule, the integral of with respect to is .
Combine fractions.
Write as a fraction with denominator .
Multiply and to get .
Since is constant with respect to , the integral of with respect to is .
By the Power Rule, the integral of with respect to is .
Write as a fraction with denominator .
Multiply and to get .
Evaluate at and at .
Evaluate at and at .
Evaluate at and at .
Simplify each term.
Simplify each term.
Raise to the power of to get .
Raising to any positive power yields .
Divide by to get .
Multiply by to get .
Simplify each term.
Raise to the power of to get .
Raising to any positive power yields .
Divide by to get .
Multiply by to get .
Cancel the common factor of .
Write as a fraction with denominator .
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Simplify.
Multiply and to get .
Divide by to get .
Simplify each term.
Reduce the expression by cancelling the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by to get .
Raise to the power of to get .
Raising to any positive power yields .
Divide by to get .
Multiply by to get .
Multiply by to get .
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 to get .
Combine the numerators over the common denominator.
Multiply by to get .
Multiply by to get .
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 to get .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by to get .
Subtract from to get .
Simplify .
Write as a fraction with denominator .
Multiply and to get .
Move to the left of the expression .
Reorder terms.

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