Questions
For let
then is given by
detailed solution
Correct option is C
Integrating by parts, we obtain Im,n=xm+1(log x)nm+101−nm+1∫01 xm(log x)n−1dxSince limx→0+ xm(log x)n=limx→0+ xm/nlog xn=0So, Im, n=−nm+1Im, n−1Hence I5, 5=−56I5, 4 =−56−46I5, 3=(−1)35.4.363I5, 2=(−1)45.4.3.264I5, 1I5, 1=∫01 x5log xdx=x6log x601−16∫01 x61xdx=−162So I5, 5=(−1)55!66=−5!66Similar Questions
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