Help with the working out : / (1 Viewer)

mikikieko12 · Jun 25, 2020

Answer is C.

pikachu975 · Jun 25, 2020

I kinda forgot how to integrate to find volume but I'm assuming you find the volume of the red+blue area rotated (cylinder volume with radius 2, height y = ln4) and minus the blue are rotated around the y axis (equation x = 0.5e^y).

mikikieko12 · Jun 25, 2020

pikachu975 said:
View attachment 28495
I kinda forgot how to integrate to find volume but I'm assuming you find the volume of the red+blue area rotated (cylinder volume with radius 2, height y = ln4) and minus the blue are rotated around the y axis (equation x = 0.5e^y).

Ohh, okay! I get it, I only applied the disc method and didn't consider the shells method. Will try and see if this will yield the right result.

Thanks a lot for the guidance!

Drongoski · Jun 25, 2020

Volume =
$$ vol of cylinder $ - \pi \int ^* _* x^2dy \\ \\ = \pi \times 2^2\times ln4 - \pi\int ^{ln4} _0 (\frac{1}{2}e^y)^2dy \\ \\ =4\pi ln4 - \frac {\pi}{4} \int _0 ^{ln4} e^{2y} dy \\ \\ = 4\pi ln4 - \frac {\pi}{8} \left [e^{2y} \right ]^{ln4} _0\\ \\ = \frac{\pi}{8}(32ln4 - 15)$

Help with the working out : / (1 Viewer)

mikikieko12

Member

Attachments

pikachu975

Premium Member

mikikieko12

Member

Drongoski

Well-Known Member

Users Who Are Viewing This Thread (Users: 0, Guests: 1)