Mathematics, 13.02.2020 03:23 isabellainksow87vn
Use the shell method to compute the volume of the solids obtained by rotating the region enclosed by the graphs of the functions y=x2 and y=8−x2 for x≥0.5 about the y-axis.
Answers: 2
and 
is
we will use the intersection x = 2 and y = 4
![V = \int\limits^2_{0.5} {2\pi x (8 - 2x^2)} \, dx\\V = 4\pi\int\limits^2_{0.5} {(4x - x^3)} \, dx\\V = 4\pi[2x^2 - x^4/4]^2_{0.5}\\V = 4\pi(2*2^2 - 2^4/4 - 2*0.5^2 + 0.5^4/4)\\V = 4\pi(8 - 4 - 0.5 + 0.015625) \approx 44.18](/tpl/images/0509/4958/98e63.png)
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