Find the volume of the indicated region.
-the region in the first octant bounded by the coordinate planes and the surface $\mathrm { z } = 64 - \mathrm { x } ^ { 2 } - \mathrm { y }$
A) $\frac { 131,072 } { 15 }$
B) 8192
C) $\frac { 32,768 } { 3 }$
D) $\frac { 65,536 } { 9 }$

Question

Quizplus · Accepted Answer

The volume is found by integrating the function $ z = 64 - x^2 - y $ over the region in the first octant. The limits for $ x $ are from 0 to 8, and for $ y $ from 0 to $ 64 - x^2 $. The correct volume is $\frac{131,072}{15}$.

Find the Volume of the Indicated Region z=64−x2−y\mathrm { z } = 64 - \mathrm { x } ^ { 2 } - \mathrm { y }z=64−x2−y

Find the Volume of the Indicated Region $\mathrm { z } = 64 - \mathrm { x } ^ { 2 } - \mathrm { y }$