InterviewSolution
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InterviewSolution
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निम्न समाकलों के मान ज्ञात कीजिए - (i) `int_(0)^(pi//4)sqrt(tan theta) d theta` |
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Answer» Correct Answer - `(1)/(2sqrt2)[log[((sqrt2-1))/((sqrt2+1))]+pi]` माना `tan theta= t^(2) rArr sec^(2) theta d theta = 2 t dt` तब ` int_(0)^(pi//4)sqrt(tan theta) d theta = int_(0)^(1)(2t^(2))/(1+t^(4))dt=int_(0)^(1)((t^(2)+1)(t^(2)-1))/(t^(4)+1)dt` `=int_(0)^(1)((1+(1)/(t^(2))))/((t^(2)+(1)/(t^(2))))dt-int_(0)^(1)((1-(1)/(t^(2))))/((t^(2)+(1)/(t^(2))))dt` `=int_(0)^(1)((1+(1)/(t^(2))))/((t-(1)/(t))^(2)+(sqrt2)^(2))dt-int_(0)^(1)((1-(1)/(t^(2))))/((t+(1)/(t))^(2)-(sqrt2)^(2))dt` अब माना `t-(1)/(t)=u` प्रथम समाकलन में तथा `t+(1)/(t)=v` द्वितीय समाकलन में |
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