Question

Find the volume V obtained by rotating the region bounded by the given curves about the specified axis.
y = sin x, y = cos x, 0 ≤ x ≤ \(\frac{π}{4}\) ; rotated about y = 1

Disk method (please feel free to check it)
\[\large V=\int\limits_{0}^{\frac{\pi}{4}} (2\pi x)((\sin (x))^2 - (\cos (x))^2) dx\]

Answer 1

Got a syntax error...

Answer 2

\[\large V=\int\limits_{0}^{\frac{\pi}{4}} (2\pi x)((\sin (x))^2 - (\cos (x))^2) dx\]?

Answer 3

your syntax error is the \ before the 4 in the fraction pi/4

Answer 4

Yeah... and except it's rotated around y=1, not y=0. Should I just repost?

Answer 5

yeah, since you closed this that may be a good idea
I'll post the \[\large V=\int\limits_{0}^{\frac{\pi}{4}} (2\pi x)((\sin (x))^2 - (\cos (x))^2) dx\]part, so just leave that blank
(I can edit your post)

Answer 6

I made it too big :(

Answer 7

And it appears I was mixing the disk method and cylinder methods too lol, ugh what a mess, I'll have to try again

Answer 8

yeah I haven't even really tried this yet
we can do it from here if you want, or repost
it's your call

Answer 9

here's our drawing... sorry for the squiggly lines; drawing feature not very good with trig graphs

Answer 10

Testing before making a new topic/question...



Find the volume V obtained by rotating the region bounded by the given curves about the specified axis. y = sin x, y = cos x, 0 ≤ x ≤ \(\frac{π}{4}\) ; rotated about y = 1

Disk method (please feel free to check it):
\[Volume= \int\pi r^2 = \int\limits_{0}^{\frac{\pi}{4}} (\pi)((1-\sin (x))^2 - (1-\cos (x))^2) dx \]
Need a bit of help with a the trig substitutions here I think... and just somebody to check this isn't blatantly incorrect.