# Find the Volume y=8x^3 , y=0 , x=1 , ,
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
Simplify the integrand.
Apply the product rule to .
Raise to the power of .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Multiply by .
Since is constant with respect to , move out of the integral.
Move to the left of .
By the Power Rule, the integral of with respect to is .
Combine and .
Substitute and simplify.
Evaluate at and at .
Simplify.
One to any power is one.
Raising to any positive power yields .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Combine and .
Combine and .
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