Solve the problem.
-Solve for a:
$$\int _ { 0 } ^ { 48 a } \int _ { 0 } ^ { a } \int _ { 0 } ^ { x ^ { 2 } } d y d x d z = 81$$
A) $a = \frac { 1 } { 2 }$
B) $a = 1$
C) $a = \frac { 3 } { 2 }$
D) $\mathrm { a } = \frac { 3 } { 4 }$

Question

Quizplus · Accepted Answer

The integral evaluates to $ \frac{a^4}{4} \times 48a = 81 $. Solving $ 12a^5 = 81 $ gives $ a = \frac{3}{2} $.

Solve the Problem ∫048a∫0a∫0x2dydxdz=81\int _ { 0 } ^ { 48 a } \int _ { 0 } ^ { a } \int _ { 0 } ^ { x ^ { 2 } } d y d x d z = 81∫048a​∫0a​∫0x2​dydxdz=81

Solve the Problem $\int _ { 0 } ^ { 48 a } \int _ { 0 } ^ { a } \int _ { 0 } ^ { x ^ { 2 } } d y d x d z = 81$