Please show work as well, I need to get an understanding :) thanks! 1. Find the
ID: 3344973 • Letter: P
Question
Please show work as well, I need to get an understanding :) thanks!
1. Find the volume of the region bounded by the graphs of x2 =y%u22122, 2y%u2212x%u22122=0, x=0 and x = 1, revolved about the x-axis.
2. Find the volume of the region in the first quadrant bounded by the graphs of y = 1 x3 and 8
y = 2x, which is revolved about the y-axis.
3. The region bounded by the graphs of y=x2 and y=x+2 is revolved about the line x=3. Express the volume of the resulting solid as a definite integral.
4. The region in the first quadrant which is bounded by the graphs of x=2y3%u2212y4 and the y-axis. This region is revolved about the x-axis. Set up the integral for the volume of the resulting solid.
Explanation / Answer
volume = pie integral(3x^2)^2 dx from x - 0 to x=1
= pie integral9x^4 dx from 0 to 1
= pie [ (9/5)x^5 ] from 0 to 1
= pie (9/5 - 0)
= 9pie/5