CBSE Class 12-science Answered

41st sum

Asked by lovemaan5500 | 10 Feb, 2020, 11:52: PM

Expert Answer

To find integral of (cos^-1x)/x²

I equals integral fraction numerator cos to the power of negative 1 end exponent x over denominator x squared end fraction d x equals integral open parentheses cos to the power of negative 1 end exponent x close parentheses 1 over x squared d x equals cos to the power of negative 1 end exponent x integral 1 over x squared d x minus integral open square brackets fraction numerator d open parentheses cos to the power of negative 1 end exponent x close parentheses over denominator d x end fraction integral 1 over x squared d x close square brackets d x equals negative fraction numerator cos to the power of negative 1 end exponent x over denominator x end fraction minus integral open square brackets fraction numerator 1 over denominator x square root of 1 minus x squared end root end fraction close square brackets d x T a k e space square root of 1 minus x squared end root equals t space rightwards double arrow space fraction numerator negative x over denominator square root of 1 minus x squared end root end fraction d x equals d t space rightwards double arrow space d x equals fraction numerator square root of 1 minus x squared end root over denominator negative x end fraction d t rightwards double arrow space d x equals fraction numerator negative t over denominator square root of 1 minus t squared end root end fraction T h e r e f o r e comma space w e space h a v e I equals negative fraction numerator cos to the power of negative 1 end exponent x over denominator x end fraction minus integral open square brackets fraction numerator 1 over denominator t squared minus 1 end fraction close square brackets d t equals negative fraction numerator cos to the power of negative 1 end exponent x over denominator x end fraction minus integral open square brackets fraction numerator 1 over denominator 2 open parentheses t minus 1 close parentheses end fraction minus fraction numerator 1 over denominator 2 open parentheses t plus 1 close parentheses end fraction close square brackets d t equals negative fraction numerator cos to the power of negative 1 end exponent x over denominator x end fraction minus 1 half open square brackets ln open parentheses t minus 1 close parentheses minus ln open parentheses t plus 1 close parentheses close square brackets equals negative fraction numerator cos to the power of negative 1 end exponent x over denominator x end fraction minus 1 half open square brackets ln open parentheses fraction numerator t minus 1 over denominator t plus 1 end fraction close parentheses close square brackets equals negative fraction numerator cos to the power of negative 1 end exponent x over denominator x end fraction minus 1 half open square brackets ln open parentheses fraction numerator square root of 1 minus x squared end root minus 1 over denominator square root of 1 minus x squared end root plus 1 end fraction close parentheses close square brackets

Answered by Renu Varma | 11 Feb, 2020, 10:32: AM

CBSE Class 12-science Answered

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CBSE Class 12-science Answered

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