, , ,

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

Apply the product rule to .

One to any power is one.

Move out of the denominator by raising it to the power.

Multiply the exponents in .

Apply the power rule and multiply exponents, .

Multiply by .

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

Evaluate at and at .

Simplify.

Rewrite the expression using the negative exponent rule .

One to any power is one.

Write as a fraction with a common denominator.

Combine the numerators over the common denominator.

Add and .

Combine and .

Find the Volume y=1/x , x=1 , x=2 , y=0