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Sir pls solve this question.

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Asked by rsudipto 11th December 2018, 9:33 AM
Answered by Expert
Answer:
f(1/x) + x2 f(x) = 0  hence begin mathsize 12px style fraction numerator f open parentheses begin display style 1 over x end style close parentheses over denominator f left parenthesis x right parenthesis end fraction space equals space minus x squared end style  , this is possible only if f(x) = 1/(ix)
Hence
begin mathsize 16px style integral f left parenthesis x right parenthesis d x space equals space 1 over i integral subscript sin theta end subscript superscript cos e c theta end superscript fraction numerator d x over denominator x end fraction space equals space 1 over i open vertical bar log space x close vertical bar subscript sin theta end subscript superscript cos e c theta end superscript space equals space 1 over i log fraction numerator cos e c left parenthesis theta right parenthesis over denominator sin left parenthesis theta right parenthesis end fraction space

equals space 1 over i log fraction numerator 1 over denominator sin squared theta end fraction space equals space minus 2 over i log space sin space theta equals space 2 i space log space sin space theta end style
Answered by Expert 13th December 2018, 4:19 PM
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