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
Simplify the integrand.
Tap for more steps...
Simplify each term.
Tap for more steps...
Rewrite as .
Expand using the FOIL Method.
Tap for more steps...
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Tap for more steps...
Simplify each term.
Tap for more steps...
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Tap for more steps...
Use the power rule to combine exponents.
Add and .
Multiply by .
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Tap for more steps...
Multiply by .
Tap for more steps...
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply by .
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Tap for more steps...
Multiply by .
Tap for more steps...
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply by .
Multiply by .
Multiply by .
Subtract from .
Apply the product rule to .
Raise to the power of .
Multiply by .
Subtract from .
Split the single integral into multiple integrals.
Since is constant with respect to , move out of the integral.
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 .
Since is constant with respect to , move out of the integral.
By the Power Rule, the integral of with respect to is .
Simplify the answer.
Tap for more steps...
Combine and .
Substitute and simplify.
Tap for more steps...
Evaluate at and at .
Evaluate at and at .
Evaluate at and at .
Simplify.
Tap for more steps...
Raise to the power of .
Raising to any positive power yields .
Cancel the common factor of and .
Tap for more steps...
Factor out of .
Cancel the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Add and .
Combine and .
Multiply by .
Raise to the power of .
Raising to any positive power yields .
Cancel the common factor of and .
Tap for more steps...
Factor out of .
Cancel the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Add and .
Combine and .
Multiply by .
Move the negative in front of the fraction.
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 .
Tap for more steps...
Multiply and .
Multiply by .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Multiply by .
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Raise to the power of .
Raising to any positive power yields .
Cancel the common factor of and .
Tap for more steps...
Factor out of .
Cancel the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Add and .
Combine and .
Multiply by .
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 .
Tap for more steps...
Multiply and .
Multiply by .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Multiply by .
Multiply by .
Add and .
Combine and .
Multiply by .
Divide by .
Enter YOUR Problem
Mathway requires javascript and a modern browser.
Cookies & Privacy
This website uses cookies to ensure you get the best experience on our website.
More Information