Find the volume of the solid that lies under the hyperbolic paraboloid z = 19 + x2 − y2 and above the rectangle. r = [−2, 2] × [0, 4].

44 cubic units

Step-by-step explanation:

we are given that a solid lies under the hyperbolic paraboloid

and above the rectangle. R = [−2, 2] × [0, 4].

Thus we see in xy plane x varies from -2 to 0, y varies from 2 to 4 while z varies from 0 to

To find volume we use triple integrals.

Using triple integral we find volume of the solid is equal to 44 cubic units.

answer: bearing in mind that a rectangle has a perimeter of length + length + width + width.

step-by-step explanation:

p = perimeter

l = length

x=width

p = 2l + 2x

p = 2(l+x)     < ==== perimeter of the base of the box.

it should be a.

hope it