Find the volume of the solid that lies between planes perpendicular to the x-axis at x = pi/4 and x = 5pi/4. the cross-sections between the planes are circular disks whose diameters run from the curve y = 2 cos x to the curve y = 2 sin x.

The volume of the solid = π²

Step-by-step explanation:

As per the given data of the questions,

The diameter of each disk is  

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

So its radius is

R = sin(x) - cos(x).

The area of each disk is

Now,

Integrate from , we get volume:

After integrate without limit we get

Now after putting the limit, we get

 V = π²

Hence, the required volume of the solid = π²

yes because there is exactly one y value for every x value

for function there can't be more than one value for every x value