Integrate the function.
-$$\int \frac { \sqrt { 64 - x ^ { 2 } } } { x ^ { 4 } } d x , x

Question

Integrate the function.
-$$\int \frac { \sqrt { 64 - x ^ { 2 } } } { x ^ { 4 } } d x , x < 8$$
A) $- \frac { 192 x ^ { 3 } } { \left( 64 - x ^ { 2 } \right) ^ { 3 / 2 } } + C$
B) $- \frac { \left( 64 - x ^ { 2 } \right) ^ { 3 / 2 } } { 192 x ^ { 3 } } + C$
C) $\frac { 64 } { \left( 64 - x ^ { 2 } \right) ^ { 1 / 2 } } + C$
D) $\frac { \left( 64 - x ^ { 2 } \right) ^ { 3 / 2 } } { x ^ { 3 } } + C$

Quizplus · Accepted Answer

The integration involves a trigonometric substitution, such as $x = 8 \sin \theta$, which simplifies the integral. After solving, the result matches option B.

Integrate the Function ∫64−x2x4dx,x<8\int \frac { \sqrt { 64 - x ^ { 2 } } } { x ^ { 4 } } d x , x < 8∫x464−x2​​dx,x<8

Integrate the Function $\int \frac { \sqrt { 64 - x ^ { 2 } } } { x ^ { 4 } } d x , x < 8$