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CBSE Class 12-science Answered

Ans is 1/2 but I need the stepwise solution

Asked by dattashibani456 | 06 Apr, 2022, 01:07: PM
Expert Answer
TO integrate the function logx sin(logx)
integral subscript 0 superscript 1 log left parenthesis x right parenthesis space sin left parenthesis log left parenthesis x right parenthesis right parenthesis space d x
equals log left parenthesis x right parenthesis integral subscript 0 superscript 1 space sin left parenthesis log left parenthesis x right parenthesis right parenthesis space d x minus integral open square brackets open curly brackets integral subscript 0 superscript 1 space sin left parenthesis log left parenthesis x right parenthesis right parenthesis space d x close curly brackets open curly brackets fraction numerator d over denominator d x end fraction left parenthesis log x right parenthesis close curly brackets close square brackets
equals log left parenthesis x right parenthesis open square brackets negative x cos left parenthesis log x right parenthesis close square brackets subscript 0 superscript 1 plus integral subscript 0 superscript 1 open square brackets x space cos open parentheses log left parenthesis x right parenthesis close parentheses cross times 1 over x d x close square brackets
equals log left parenthesis x right parenthesis open square brackets negative x cos left parenthesis log x right parenthesis close square brackets subscript 0 superscript 1 space plus integral subscript 0 superscript 1 open square brackets cos open parentheses log left parenthesis x right parenthesis close parentheses close square brackets d x
equals open square brackets negative log left parenthesis x right parenthesis x cos left parenthesis log x right parenthesis close square brackets subscript 0 superscript 1 space plus open square brackets x sin left parenthesis log x right parenthesis close square brackets subscript 0 superscript 1 space
equals negative log 1 cross times 1 cross times cos left parenthesis log 1 right parenthesis plus 0 plus sin left parenthesis log 1 right parenthesis minus 0
equals sin 0
equals straight pi over 2
Answered by Renu Varma | 11 Apr, 2022, 12:29: PM
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