Respuesta :
Answer:
44 cubic units
Step-by-step explanation:
we are given that a solid lies under the hyperbolic paraboloid
[tex]z = 19 + x^2 - y^2[/tex]
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 [tex]19 + x^2 - y^2[/tex]
To find volume we use triple integrals.
[tex]V=\int_2^4 \int_{-2} ^0 \int_0^{19 + x^2 - y^2} dzdxdy\\= \int_2^4 \int_{-2} ^0 (19 + x^2 - y^2} dxdy\\= \int_2^4 19x+\frac{x^3}{3} -xy^2 dy \\=\int_2^4 38-2y^2+\frac{8}{3} dy\\=38y-\frac{2y^3}{3} +\frac{8y}{3}\\=44[/tex]
Using triple integral we find volume of the solid is equal to 44 cubic units.
