![displaystyleint dfrac{sqrt{x^2-a^2}}{x}dx= ______.sqrt{x^2-a^2}+asec^{-1}left(dfrac{x}{a}right)+csqrt{x^2-a^2}-acos^{-1}left(dfrac{a}{x}right)+cxsqrt{x^2-a^2}-dfrac{1}{a}tan^{-1}left(dfrac{x}{a}right)+csqrt{x^2-a^2}+dfrac{1}{x}sec^{-1}(x)+c displaystyleint dfrac{sqrt{x^2-a^2}}{x}dx= ______.sqrt{x^2-a^2}+asec^{-1}left(dfrac{x}{a}right)+csqrt{x^2-a^2}-acos^{-1}left(dfrac{a}{x}right)+cxsqrt{x^2-a^2}-dfrac{1}{a}tan^{-1}left(dfrac{x}{a}right)+csqrt{x^2-a^2}+dfrac{1}{x}sec^{-1}(x)+c](https://search-static.byjusweb.com/question-images/toppr_ext/questions/1410308_1675829_ans_693bf3e91eb7453593cfc1619f931a93.jpg)
displaystyleint dfrac{sqrt{x^2-a^2}}{x}dx= ______.sqrt{x^2-a^2}+asec^{-1}left(dfrac{x}{a}right)+csqrt{x^2-a^2}-acos^{-1}left(dfrac{a}{x}right)+cxsqrt{x^2-a^2}-dfrac{1}{a}tan^{-1}left(dfrac{x}{a}right)+csqrt{x^2-a^2}+dfrac{1}{x}sec^{-1}(x)+c
Prove that: displaystyle int sqrt {a^{2} - x^{2}}dx = dfrac {x}{2}sqrt {a^{2} - x^{2}} + dfrac {a^{2}}{2}sin^{-1} left (dfrac {x}{a}right ) + c
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Integration of Square Root of a^2-x^2 |Integral of Square Root of Quadratic Function |#RootOfa^2-x^2 - YouTube
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![Change the integral sqrt (x^2+y^2) over the limits y=(0 to sqrt(a^2-x^2) ans x=(-a to a) into polars and hence evaluate its value – Yawin Change the integral sqrt (x^2+y^2) over the limits y=(0 to sqrt(a^2-x^2) ans x=(-a to a) into polars and hence evaluate its value – Yawin](https://www.yawin.in/wp-content/uploads/2023/03/SI10-785x1024.jpg)
Change the integral sqrt (x^2+y^2) over the limits y=(0 to sqrt(a^2-x^2) ans x=(-a to a) into polars and hence evaluate its value – Yawin
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