Deriving formulas Evaluate the following integrals. Assume

Chapter 7, Problem 76AE

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QUESTION:

Deriving formulas Evaluate the following integrals. Assume a and b are real numbers and n is an integer.

\(\int x^{n} \sin ^{-1} x \ d x\); Use integration by parts.

Questions & Answers

QUESTION:

Deriving formulas Evaluate the following integrals. Assume a and b are real numbers and n is an integer.

\(\int x^{n} \sin ^{-1} x \ d x\); Use integration by parts.

ANSWER:

Answer

We have to evaluate the integral

 

 =n               (Take a constant out) ….(1)

  Apply integration by parts

  ….(2)

Now put u=

         

 ]

      ]     ……(3)

Now we evaluate the integral separately

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