Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 4 − x2 and the plane y = 2.

We use triple integration to find volume of solid.

Volume of the solid in the first octant is 32/ 3

To solve this, it is important to set up the boundaries of double integral correctly.

First, notice that the cylinder we are given intersects the XY plane at the line given by the equation x = 2

Hence our boundaries of the integral with respect to x is the segment [0,2]. Since the other plane is y=2 . so,  boundaries of the integral with respect to y is the segment [0,2].

Now , integrate that

Learn more:

link

arithmetic sequence: a sequnce in which the diffrence between any two consecutive terms is the same

step-by-step explanation:

-6 is the correct option from the above given options