Integrate the function.
-$$\int _ { 0 } ^ { 1 } \frac { d x } { \sqrt { 81 - x ^ { 2 } } }$$
A) $\frac { 1 } { 9 } \sin ^ { - 1 } \frac { 1 } { 9 }$
B) $\cos ^ { - 1 } \frac { 1 } { 9 }$
C) $9 \cos ^ { - 1 } \frac { 1 } { 9 }$
D) $\sin ^ { - 1 } \frac { 1 } { 9 }$

Question

Quizplus · Accepted Answer

The integral $\int _ { 0 } ^ { 1 } \frac { d x } { \sqrt { 81 - x ^ { 2 } } }$ can be solved by recognizing it as a standard form of the inverse trigonometric function $\sin^{-1}(x/a)$, where $a = 9$ in this case. The correct answer is $\sin ^ { - 1 } \frac { 1 } { 9 }$, as it directly follows from the substitution $x = 9\sin(\theta)$, leading to the evaluation of the integral in terms of $\sin^{-1}$.

Integrate the Function ∫01dx81−x2\int _ { 0 } ^ { 1 } \frac { d x } { \sqrt { 81 - x ^ { 2 } } }∫01​81−x2​dx​

Integrate the Function $\int _ { 0 } ^ { 1 } \frac { d x } { \sqrt { 81 - x ^ { 2 } } }$