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.

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.

turingtest · Answer

|dw:1340466830533:dw|this region, right?