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a
f(x)=(1/2)x2−1
b
g(x)=logx
c
L = 1
d
none of these
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Correct option is A
The given integral equals ∫xlogx+1xdx=∫xlog(x+1)dx−∫xlogxdx=x22log(x+1)−12∫x2x+1dx−x22logx+12∫x2xdx=x22log(x+1)−x22logx−12∫x−1+1x+1dx+12∫xdx=x22log(x+1)−x22logx+x2−12log(x+1)+C⇒f(x)=x22−12,g(x)=−12logx and L=12.Similar Questions
is equal to
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