Find the Value of the Integral $\int _ { 0 } ^ { 1 / 2 } \frac { \sin ^ { - 1 } x } { \sqrt { 1 - x ^ { 2 } } } d x$

question 181

Multiple Choice

Find the value of the integral $\int _ { 0 } ^ { 1 / 2 } \frac { \sin ^ { - 1 } x } { \sqrt { 1 - x ^ { 2 } } } d x$

• A) \(\frac { \pi ^ { 2 } } { 36 }\)
• B) \(\frac { \pi } { 36 }\)
• C) \(\frac { 1 } { 36 }\)
• D) \(\frac { \pi } { 6 }\)
• E)
• \(\frac { \pi ^ { 2 } } { 72 }\)
• F) \(\frac { \pi } { 72 }\)
• G) \(\frac { 1 } { 72 }\)
• H) \(\frac { \pi } { 2 }\)

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Definitions:

Cash Flows

The total amount of money being transferred into and out of a business, affecting the company's liquidity.

Internal Rate

The rate of return that makes the net present value (NPV) of all cash flows from a particular project equal to zero, often used in capital budgeting to assess potential investments.

Cash Flows

The entire sum of money flowing in and out of an enterprise, notably affecting its ability to meet short-term obligations.

IRR

Internal Rate of Return; a financial metric used to estimate the profitability of potential investments.