Question

find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the -axis. Verify your results using the integration capabilities of a graphing utility.
y=cosx x=pi/2 y=0 x=0

Answer 1

\[\pi \int\limits_{0}^{\pi/2} (cosx)^2\]

Answer 2

My main question is how does (cosx)^2=1/2(cos2x+1)

Answer 3

your axis of rotation is missing again, its not a copyable character and you need to actually type it in.

Answer 4

sorry its the x axis again. I did the first step already.

Answer 5

I have the work, i just dont understand how (cosx)^2=1/2(cos2x+1).

Answer 6

its a trig identity

Answer 7

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

this is why you take trig before calculus, and some classess call it pre calculus

Answer 8

if a=b=x

cos(x+x) = cos(x)cos(x) - sin(x)sin(x)

cos(2x) = cos^2 (x) - sin^2 (x)

now sin^2 + cos^2 = 1 sooo; sin^2 = 1 - cos^2

cos(2x) = cos^2 - (1-cos^2)

cos(2x) = cos^2 - 1 +cos^2

cos(2x) = 2 cos^2 - 1

can you solve the algebra for cos^2?

Answer 9

1/2 (cos(2x)+1) is simpler to play with and solve an integral for than cos^2(x)

unless you want to try integration by parts

Answer 10

Yes i think i got it now. I did take pre calc, but I am not sure I learned this. I did learn trig though.

Answer 11

trig is like 98% memorization :) its easy to forget some stuff

Answer 12

All I really remember from trig is the Pythagorean Identities and other basic things.

Answer 13

But i understand now, thanks.

Answer 14

youre welcome