Answer to Question #131625 in Calculus for Nick

Question #131625
Use cylindrical shells to find the volume of the solid that results when the region enclosed by x = y^2 and x = y is revolved about the line y= -1
1
Expert's answer
2020-09-07T17:25:33-0400

Horizontal axis of revolution


V=2πcdp(y)h(y)dyV=2\pi\displaystyle\int_{c}^dp(y)h(y)dy

y2=y=>y1=0,y2=1y^2=y=>y_1=0, y_2=1

p(y)=y(1)=y+1p(y)=y-(-1)=y+1

h(y)=yy2h(y)=y-y^2


V=2π01(y+1)(yy2)dy=V=2\pi\displaystyle\int_{0}^1(y+1)(y-y^2)dy=

=2π01(y2y3+yy2)dy==2\pi\displaystyle\int_{0}^1(y^2-y^3+y-y^2)dy=

=2π[y22y44]10=12π (units3)=2\pi\big[\dfrac{y^2}{2}-\dfrac{y^4}{4}\big]\begin{matrix} 1 \\ 0 \end{matrix}=\dfrac{1}{2}\pi\ (units^3)


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Comments

Assignment Expert
08.09.20, 01:44

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Nick
08.09.20, 01:37

Thanks it helps a lot

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