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Question

If Im=10xmtan1x dx

then (m+1)Im+(m1)Im2 is?

A
π4
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B
πm12
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C
π21m
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D
None of these
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Solution

The correct option is C π21m

Im=10xmtan1xdx


=[xm+1tan1xm+1]101m+110xm+11+x2dx


Im(m+1)=π410xm+11+x2dx(i)


replacing mm2in(i)


(m1)Im2=π410xm11+x2dx(ii)


(m+1)Im+(mI)Im2


π410xm+11+x2dx+π410xm11+x2dx


π210xm+1+xm11+x2dx


=π210xm1(1+x2)1+x2dx


=π210xm1dx


=π21m


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