Set up an integral of the form dc h2(y) h1(y) f(x, y) dx dy
for the volume of the region enclosed by the surfaces z = 2 - x2 - y2 and z = 2x + 2y. What is h2(0)+f(0,0)?
A. 5.
B. 13 + 2.
C. V2+1.
D. V3+1.
E. V2 + 2.

Option D.

Step-by-step explanation:

The given integral is:

The intersection curves enclosed by the surfaces:

z = 2 - x² - y² and z = 2x + 2y

This implies that:

We will realize that the curve of this intersection is a circle which is centered at (-1, -1) of the radius 2.

So, from equation (1)

x + 1 = ±

Now,

and

,  and:

and

The surface z = 2-x²-y² lies above z = 2x + 2y in the region of intersection

∴

So, h₂ (0) + f(0,0) =

h₂ (0) + f(0,0) =

5x+2x=49

7x=49

x=7. 35 apples