Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Problem with revolution of curves about an axis?
I've got the following equations:
y=x^3
y=x
and I've been asked to revolve them about the x-axis and find the volume.
I came up with:
V=integral (from 0->1) of π[x-x^3] dx
which comes out to π/4. My book says the answer is 4π/21. What have I done wrong?
1 Answer
- intc_escapeeLv 71 decade agoFavorite Answer
The intersections of y=x and y=x³ are at x = -1, x = 0, and x = 1. Based on the answer, it would seem the author is only interested in revolving the area between x = 0 and x = 1.
V = π ∫ (x)² - (x³)² dx [0,1]
= π (x³3/3 - x^7/7) [0,1]
= π (1/3 - 1/7)
= 4π/21
Answer: 4π/21 units³
