SOLUTION: The region bounded by 𝑦 = −1, 𝑦 = 𝑒^2x, x = 0 and 𝑥 = 2 is revolved about the line 𝑦 = −1. Find the volume of the resulting solid.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The region bounded by 𝑦 = −1, 𝑦 = 𝑒^2x, x = 0 and 𝑥 = 2 is revolved about the line 𝑦 = −1. Find the volume of the resulting solid.      Log On


   

Question 1208486: The region bounded by 𝑦 = −1, 𝑦 = 𝑒^2x, x = 0 and 𝑥 = 2 is revolved about the line 𝑦 = −1. Find the volume of the resulting solid.
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
We use the Washer Method. The distance from the graph to the revolving line is e%5E%282x%29%2B1, so we have the volume as pi%2Aint%28%28e%5E%282x%29%2B1%29%5E2%2Cdx%2C0%2C2%29. That is equal to pi%2Aint%28e%5E%284x%29%2B2%2Ae%5E%282x%29%2B1%2Cdx%2C0%2C2%29. The integral of the expression can be calculated to be e%5E%284x%29%2F4%2Be%5E%282x%29%2Bx, and with the bounds, we have the volume as pi%2A%28%28e%5E8%2F4%2Be%5E4%2B2%29-%281%2F4%2B1%29%29. Plugging this into a calculator gives the approximate answer of 2515.1203 (rounded to 4 decimal places).