CBSE Class 12-science Answered
integrate under root a^2 - x^2 dx =
Asked by manasvichandel49 | 19 Oct, 2023, 08:53: AM
Let ![begin mathsize 14px style I space equals space integral fraction numerator d x over denominator square root of a squared minus x squared end root end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/0a817482815f45b7d11b9b677b15de76.png)
![begin mathsize 14px style I space equals space integral fraction numerator d x over denominator square root of a squared minus x squared end root end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/0a817482815f45b7d11b9b677b15de76.png)
Let us use the substitution x = a cosθ
dx = -a sinθ dθ
Then above integration becomes
![begin mathsize 14px style I space equals integral space fraction numerator negative a space sin theta space d theta over denominator a space sin theta end fraction space equals space minus integral space d theta space equals space minus theta space equals space minus space cos to the power of negative 1 end exponent left parenthesis x divided by a right parenthesis end style](https://images.topperlearning.com/topper/tinymce/cache/34cbe186eb36b024511993176647e019.png)
Answered by Thiyagarajan K | 19 Oct, 2023, 21:55: PM
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