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CBSE Class 12-science Answered

Integrate.    x arcsinx dx
Asked by Harsh | 25 Jul, 2019, 07:02: AM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral xsin to the power of negative 1 end exponent xdx straight I equals integral sin to the power of negative 1 end exponent straight x space cross times xdx straight I equals sin to the power of negative 1 end exponent straight x integral xdx minus integral open parentheses fraction numerator dsin to the power of negative 1 end exponent straight x over denominator dx end fraction integral xdx close parentheses dx straight I equals straight x squared over 2 sin to the power of negative 1 end exponent straight x minus integral fraction numerator 1 over denominator square root of 1 minus straight x squared end root end fraction straight x squared over 2 dx straight I equals straight x squared over 2 sin to the power of negative 1 end exponent straight x minus 1 half integral fraction numerator straight x squared over denominator square root of 1 minus straight x squared end root end fraction dx Integrating space further space we space get straight I equals straight x squared over 2 sin to the power of negative 1 end exponent straight x plus straight x over 4 square root of 1 minus straight x squared end root plus 1 fourth sin to the power of negative 1 end exponent straight x plus straight c end style
Answered by Sneha shidid | 25 Jul, 2019, 09:51: AM

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