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=1, and y=1 is revolved around the line y=-2?

Answer 1

The fourth option is correct.

See the attached image. The red cylinder represents a washer formed by the described revolution. Its volume is

$\pi((\text{outer radius})^2-(\text{inner radius})^2)(\text{height})$

so when we integrate, we take

$\displaystyle\pi\int_0^1((e^x+2)^2-3^2)\,\mathrm dx$