- #1
James889
- 192
- 1
Hi,
The area
[tex]e^x-1[/tex]
Is rotated about the y axis, bounded by y=1, x=0 and x=ln2 find the volume of the solid.
And i am clearly making something wrong, so if anyone could verify my work.
[tex]~ 2\pi\int_0^{ln2}x\cdot(1-(e^x-1)[/tex]
[tex]-2\pi\int_0^{ln2}xe^x-2x[/tex]
Integration:
u=x, du=1
dv=e^x, v=e^x
[tex]\int xe^x -2x= xe^x -e^x -x^2[/tex]
[tex]e^x(x-1)-x^2\bigg|_0^{ln2} = 2\pi \cdot ln2-1 -(ln2)^2[/tex]
The answer is supposed to be [tex]2\pi(ln2-1)^2[/tex]
Thanks!
The area
[tex]e^x-1[/tex]
Is rotated about the y axis, bounded by y=1, x=0 and x=ln2 find the volume of the solid.
And i am clearly making something wrong, so if anyone could verify my work.
[tex]~ 2\pi\int_0^{ln2}x\cdot(1-(e^x-1)[/tex]
[tex]-2\pi\int_0^{ln2}xe^x-2x[/tex]
Integration:
u=x, du=1
dv=e^x, v=e^x
[tex]\int xe^x -2x= xe^x -e^x -x^2[/tex]
[tex]e^x(x-1)-x^2\bigg|_0^{ln2} = 2\pi \cdot ln2-1 -(ln2)^2[/tex]
The answer is supposed to be [tex]2\pi(ln2-1)^2[/tex]
Thanks!