Calculus question, please help thank you in advance

Question

Which of the following integrals will find the volume of the solid that is formed when the region bounded by the graphs of y = e^x, x = 2, and y = 1 is revolved around the line y = −1.

a. 

b.  

c.

 d.

Answer 1

The volume of a cylinder is πr²h. The h is dx in this case.

The radius 'r' of the outer shell is e^x. The radius of the inner shell is (1 - (-1)) = 2.

Therefore, the volume is

π∫((e^x)² - 2²)dx = π∫((e^2x) - 2²)dx

Choice A.

Answer 2

By Disk Mathod V = π∫₀^2[(e^x + 2)² - 4]dx = π∫₀²(e^2x + 4e^x)dx = π(e^2x/2 + 4e^x)₀² = π(e⁴/2 + 4e² - 1/2 - 4) =

= 164.479