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Asked by inderjeet.saluja | 27th Aug, 2014, 12:02: AM

Expert Answer:

 integral fraction numerator sin to the power of minus 1 space space end exponent square root of x space end root space space space minus cos space to the power of minus 1 end exponent square root of x over denominator sin to the power of minus 1 space space end exponent square root of x space end root space space space plus cos space to the power of minus 1 end exponent square root of x end fraction d x................. left parenthesis i right parenthesis  P u t space sin to the power of minus 1 space space end exponent square root of x space end root space space space equals space theta square root of x space end root space equals sin space theta x equals space sin squared theta d x space equals 2 sin space theta cos space theta d theta  cos space to the power of minus 1 end exponent square root of x equals cos to the power of minus 1 end exponent left parenthesis sin space space theta right parenthesis equals cos to the power of minus 1 end exponent left parenthesis cos left parenthesis 90 minus theta right parenthesis right parenthesis equals 90 space minus theta P u t t i n g space v a l u e s space o f space sin to the power of minus 1 space space end exponent square root of x space end root a n d space cos space to the power of minus 1 end exponent square root of x space space space i n space left parenthesis i right parenthesis space w e space g e t comma  integral fraction numerator theta minus 90 plus theta over denominator theta plus 90 minus theta end fraction 2 sin space theta cos space theta d theta equals integral fraction numerator 2 theta minus 90 over denominator 90 end fraction sin space 2 theta space d theta equals integral fraction numerator 2 theta sin space 2 theta over denominator 90 end fraction minus 1 over 45 integral sin space 2 theta d theta space plus integral sin space 2 theta d theta  equals integral fraction numerator theta sin space 2 theta over denominator 45 end fraction minus 1 over 45 integral sin space 2 theta d theta minus fraction numerator cos space 2 theta over denominator 2 end fraction   equals minus fraction numerator theta cos space 2 theta over denominator 90 end fraction plus fraction numerator cos 2 theta over denominator 90 end fraction minus fraction numerator cos space 2 theta over denominator 2 end fraction plus c   equals minus fraction numerator sin to the power of minus 1 space space end exponent square root of x space end root cos space left parenthesis 2 sin to the power of minus 1 space space end exponent square root of x space end root right parenthesis over denominator 90 end fraction minus fraction numerator 22 cos left parenthesis 2 sin to the power of minus 1 space space end exponent square root of x space right parenthesis end root over denominator 45 end fraction plus c

Answered by Sanjana Dhopatkar | 27th Aug, 2014, 09:05: AM