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Sir pls solve the following.
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Asked by rsudipto | 01 Jan, 2019, 10:19: AM
answered-by-expert Expert Answer
begin mathsize 12px style I space equals space integral fraction numerator p space x to the power of p plus 2 q minus 1 end exponent space minus space q space x to the power of q minus 1 end exponent over denominator open parentheses x to the power of 2 p plus 2 q end exponent plus 2 x to the power of p plus q end exponent plus 1 close parentheses end fraction space d x space D e n o m i n a t o r space o f space i n t e g r a n d space colon space open parentheses x to the power of 2 p plus 2 q end exponent plus 2 x to the power of p plus q end exponent plus 1 close parentheses space equals space open parentheses space x to the power of p plus q end exponent plus 1 close parentheses squared w e space m o d i f y space t h e space n u m e r a t o r space o f space i n t e g r a n d space colon space N r space equals space space space p space x to the power of p plus 2 q minus 1 end exponent space minus space q space x to the power of q minus 1 end exponent space minus space q space x to the power of p plus 2 q minus 1 end exponent space plus space q space x to the power of p plus 2 q minus 1 end exponent space N r space equals space open parentheses p plus q close parentheses space x to the power of p plus 2 q minus 1 end exponent space minus q space x to the power of q minus 1 end exponent left parenthesis 1 plus x to the power of p plus q end exponent right parenthesis I space equals space integral space open curly brackets fraction numerator open parentheses p plus q close parentheses begin display style begin display style x end style to the power of p plus 2 q minus 1 end exponent end style over denominator begin display style open parentheses x to the power of p plus q end exponent plus 1 close parentheses squared end style end fraction space minus space fraction numerator q space x to the power of q minus 1 end exponent over denominator open parentheses x to the power of p plus q end exponent plus 1 close parentheses end fraction close curly brackets d x space equals space I subscript 1 space minus space I subscript 2 w h e r e space I subscript 1 space equals space integral fraction numerator begin display style open parentheses p plus q close parentheses x to the power of p plus 2 q minus 1 end exponent end style over denominator begin display style open parentheses x to the power of p plus q end exponent plus 1 close parentheses squared end style end fraction d x space space space space space space a n d space space space space space space I subscript 2 space equals space integral fraction numerator begin display style q space x to the power of q minus 1 end exponent end style over denominator begin display style open parentheses x to the power of p plus q end exponent plus 1 close parentheses end style end fraction d x I subscript 2 space equals space integral fraction numerator begin display style q space x to the power of q minus 1 end exponent end style over denominator begin display style open parentheses x to the power of p plus q end exponent plus 1 close parentheses end style end fraction d x space equals space integral fraction numerator d left parenthesis x to the power of q right parenthesis over denominator x to the power of p plus q end exponent plus 1 end fraction space equals space fraction numerator x to the power of q over denominator x to the power of p plus q end exponent plus 1 end fraction space space plus integral space x to the power of q space open parentheses x to the power of p plus q end exponent plus 1 close parentheses to the power of negative 2 end exponent left parenthesis p plus q right parenthesis x to the power of p plus q minus 1 end exponent d x I subscript 2 space equals space fraction numerator begin display style x to the power of q end style over denominator begin display style x to the power of p plus q end exponent plus 1 end style end fraction space space plus space integral fraction numerator begin display style open parentheses p plus q close parentheses x to the power of p plus 2 q minus 1 end exponent end style over denominator begin display style open parentheses x to the power of p plus q end exponent plus 1 close parentheses squared end style end fraction d x space equals space space fraction numerator begin display style x to the power of q end style over denominator begin display style x to the power of p plus q end exponent plus 1 end style end fraction space plus space I subscript 1 H e n c e space I space equals space I subscript 1 space minus space I subscript 2 space equals space minus space fraction numerator begin display style x to the power of q end style over denominator begin display style x to the power of p plus q end exponent plus 1 end style end fraction space plus space C end style
Answered by Thiyagarajan K | 01 Jan, 2019, 16:31: PM

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