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CBSE Class 12-science Answered

integrate under root a^2 - x^2 dx =
Asked by manasvichandel49 | 19 Oct, 2023, 08:53: AM
answered-by-expert Expert Answer
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
 
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
 
 
Answered by Thiyagarajan K | 19 Oct, 2023, 21:55: PM
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integral fraction numerator sin x times cos x over denominator square root of 1 plus sin squared end root x end fraction d x
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