Question

Calculate the volume of the rotating body formed by rotating the region bounded by the curve $y=x-x^{2}$ and the lines $y=0, x=2$ about the $\mathrm{x}$-axis. a) $\frac{\pi}{15}$ b) $\frac{\pi}{10}$ c) $\frac{\pi}{12}$ d) $\frac{\pi}{30}$ e) $\frac{\pi}{6}$

Name: calculate the volume of the rotating body formed by rotating the region bounded by the curve yx x2 and the lines y0 x2 about the mathrmx axis a fracpi15 b fracpi10 c fracpi12 d fracpi30 e fracpi6
Uploaded: 2024-04-17T11:58:55-08:00
Duration: 4 min 46 s
Channel: Willis James
Description: calculate the volume of the rotating body formed by rotating the region bounded by the curve yx x2 and the lines y0 x2 about the mathrmx axis a fracpi15 b fracpi10 c fracpi12 d fracpi30 e fracpi6

          Calculate the volume of the rotating body formed by rotating the region bounded by the curve $y=x-x^{2}$ and the lines $y=0, x=2$ about the $\mathrm{x}$-axis.  
a) $\frac{\pi}{15}$  
b) $\frac{\pi}{10}$  
c) $\frac{\pi}{12}$  
d) $\frac{\pi}{30}$  
e) $\frac{\pi}{6}$

Added by Bilge H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Willis James

04/17/2024

Step 1

We need to calculate the volume of the solid formed by rotating the region bounded by the curve $y = x - x^2$, the line $y = 0$, and the line $x = 2$ around the x-axis. This is a typical problem that can be solved using the method of disks or washers. Show more…

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Calculate the volume of the rotating body formed by rotating the region bounded by the curve $y=x-x^{2}$ and the lines $y=0, x=2$ about the $\mathrm{x}$-axis. a) $\frac{\pi}{15}$ b) $\frac{\pi}{10}$ c) $\frac{\pi}{12}$ d) $\frac{\pi}{30}$ e) $\frac{\pi}{6}$