Question

find the volume of the solid generated by rotating the region bounded by y= cos x, y=0, x=0, and x= pi/2 about y-axis

Answer 1

are you told to use a specific method?

Answer 2

slice,disk, washer........

Answer 3

I don't think you can get an exact answer.

Answer 4

I think you can only set up an integral and approximate it by simpsons or trapeziodal rule.

Answer 5

V= pi integral x^2 dy

Answer 6

please help i really dont know this

Answer 7

\[ V= \pi \int\limits_{0}^{1} (\cos^{-1} (y) )^2 dy\]

Answer 8

You can't evaluate it exactly. All you can do is approximate it.

Probably use simpsons rule with 5 function values, should give a pretty good answer.

Answer 9

that;s if it was about the x axis.

Answer 10

it says about y axis.

Answer 11

sorry ... need my morning coffee

Answer 12

maybe the asker made a typo.

Answer 13

But even so, this integral is doable. Use integration by parts twice.

First time with u' = 1, v = arccos^2(x).
Remember that (d/dx)(arccos x) = -1/sqrt(1-x^2)

Answer 14

how do you rotate the y=cos x about y-axis?

Answer 15

i think its washer if you rotate it about y-axis

Answer 16

It is disk method if you rotate it about x or y axis