Use a CAS integration utility to evaluate the triple integral of the given function over the specified solid region.
-$F ( x , y , z ) = 8 x - 8 y ^ { 2 } + 7 z ^ { 3 }$ over the rectangular solid $0 \leq x \leq 2,0 \leq y \leq 9,0 \leq z \leq 3$
A) $- \frac { 52,083 } { 4 }$
B) $- 11,574$
C) $- \frac { 34,722 } { 5 }$
D) $- \frac { 17,361 } { 2 }$

Question

Quizplus · Accepted Answer

To solve the triple integral of $F(x, y, z) = 8x - 8y^2 + 7z^3$ over the specified rectangular solid, we integrate the function with respect to $x$, $y$, and $z$ in their respective limits. The integration process involves calculating the integral of $8x$ from 0 to 2, the integral of $-8y^2$ from 0 to 9, and the integral of $7z^3$ from 0 to 3, and then multiplying the results together. The correct answer is obtained by performing these integrations and summing the results, leading to $- \frac { 17,361 } { 2 }$.

Use a CAS Integration Utility to Evaluate the Triple Integral F(x,y,z)=8x−8y2+7z3F ( x , y , z ) = 8 x - 8 y ^ { 2 } + 7 z ^ { 3 }F(x,y,z)=8x−8y2+7z3

Use a CAS Integration Utility to Evaluate the Triple Integral $F ( x , y , z ) = 8 x - 8 y ^ { 2 } + 7 z ^ { 3 }$