Mathematics, 01.06.2020 05:57 kiasiab17
Let s be the solid obtained by rotating the region shown in the figure about the y-axis (Assume a = 5 and b = 2)
Sketch a typical approximating shell.
What are its circumference c and height h?
c(x) =
h(x) =
Use shells to find the volume V of S.
V =
Answers: 2
.
![v = 10\pi \ [ \dfrac{x^{5}}{5} + \dfrac{4x^{3}}{3} - x^{4}]^{2}_0\\\\v = 10\pi [ \dfrac{2^{5}}{5} + \dfrac{4.2^{3}}{3} - 2^{4} - \dfrac{0^{5}}{5} -\dfrac{4.0^{3}}{3} + 0^{4}]}\\\\v = 10\pi \ [ \dfrac{32}{5} + \dfrac{32}{3} - 16 -0-0+0]\\\\v = 10\pi [\dfrac{96+160-240}{15}]\\\\v = 10\pi [\dfrac{16}{15}]\\\\v = \dfrac{32\pi }{3}](/tpl/images/0673/0274/bc849.png)
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