Answer to Question #151570 in Calculus for Joshua

Question #151570
Find the volume generated by revolving the area bounded by y=e^x, x=1, x=0, about y-axis. Sketch the curve indicating the generating area.
1
Expert's answer
2020-12-21T17:00:06-0500
y=ex,x=0,x=1y=e^x, x=0, x=1

V=012πx(ex)dxV=\displaystyle\int_{0}^12\pi x(e^x)dx

xexdx\displaystyle\int xe^xdx


udv=uvvdu\int udv=uv-\int vdu

u=x,du=dxu=x, du=dx

dv=exdx,v=exdx=exdv=e^xdx, v=\displaystyle\int e^xdx=e^x


xexdx=xexexdx=xexex+C\displaystyle\int xe^xdx=xe^x-\displaystyle\int e^xdx=xe^x-e^x+C

V=012πx(ex)dx=2π[xexex]10V=\displaystyle\int_{0}^12\pi x(e^x)dx=2\pi\big[xe^x-e^x\big]\begin{matrix} 1 \\ 0 \end{matrix}

=2π(ee(01))=2π(units3)=2\pi(e-e-(0-1))=2\pi (units^3)

V=2π cubic unitsV=2\pi\ cubic\ units



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment