The region under the curves $y = cos x - sin x, 0 \leq x \leq \frac{π}{4}$ $y=cosx-sinx, 0<=x<=pi/4$ is rotated about the x axis. How do you sketch the region and find the volumes of the two solids of revolution?

Question

6282 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-22T03:49:22

volume = integration of[(pi*((cosx - sinx)^2)dx] from x = 0 to x = pi/4

volume = integration of[(pi*(1- sin2x)dx] from x = 0 to x = pi/4

volume = [(pi*(x + cos2x/2)] from x = 0 to x = pi/4

volume = [(pi(pi/4 + cospi/2)] -[(pi(0/4 + cos0/2)]
volume = [(pi(pi/4 +0)] -[(pi(0 + 1)]
volume =pi^2/4 -pi

The region under the curves y=cosx−sinx,0≤x≤π4y=cosx-sinx, 0<=x<=pi/4 is rotated about the x axis. How do you sketch the region and find the volumes of the two solids of revolution?