InterviewSolution
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InterviewSolution
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निम्न फलनों के मान ज्ञात कीजिये - `int_(1)^(2)x log x dx` |
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Answer» माना `I=int_(1)^(2)xlog x dx` log x को प्रथम फलन मानकर खण्डशः समाकलन करने से, `I=[logxint_(1)^(2)x dx-int_(1)^(2){(d)/(dx)logx int x dx}dx]` `=[(x^(2))/(2)logx]_(1)^(2)-[int_(1)^(2)(1)/(x).(x^(2))/(2)dx]` `=(1)/(2)[x^(2)logx]_(1)^(2)-(1)/(2)[int_(1)^(2)xdx]` `=(1)/(2)[x^(2)logx]_(1)^(2)-(1)/(4)[x^(2)]_(1)^(2)` `=(1)/(2)[4log2-1log1]-(1)/(4)[2^(2)-1^(2)]` `=2log 2-(3)/(4)` |
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