InterviewSolution
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InterviewSolution
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`int(dx)/(sin^(4)x + cos^(4)x)`का मान ज्ञात कीजिए। |
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Answer» माना `I = (dx)/(sin^(4) x+cos^(4)x)` अश व हर को `cos^(4)x` से भाग देंने पर `I =int(sec^(4)xdx)/(1+tan^(4)x)` `= int((1+tan^(2)x)sec^(2)xdx)/(1+tan^(4)x)` माना `x = t therefore" "sec^(2) xdx = dt` `therefore" "I int((1+t^(2))/(1+t^(4)))dt` अश व हर को `t^(2)` से भाग देने पर `I = int(1+1//t^(2))/(t^(2) + 1//t^(2))dt` माना `t - (1)/(t) =urArr (1+(1)/(t^(2)))dt= du` पुन: `t^(2) +(1)/(t^(2)) = t^(2) +(1)/(t^(2)) -2+2` ` = (t -(1)/(t))^(2) +2 = u^(2) + 2` `therefore I = int(du)/(2+u^(2))= (1)/(sqrt(2))tan^(-1)((u)/(sqrt(2)))` ` = (1)/(sqrt(2))tan^(-1)[(1)/(sqrt(2))(t-(1)/(t))] = (1)/(sqrt(2))tan^(-1).((t^(2)-1)/(tsqrt(2)))` ` = (1)/(sqrt(2))^(-1)((tan^(2)x-1)/(sqrt(2)tanx))` |
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