A) 3/2
B) 1
C) 5/4
D) -3/4
Correct Answer: D
Solution :
[d] We have \[\int\limits_{0}^{2}{f(x)dx=\frac{3}{4}};\] Now, \[\int\limits_{0}^{2}{xf'(x)dx=\,\,x\int\limits_{0}^{2}{f'(x)dx}-\int\limits_{0}^{2}{f(x)dx}}\] \[=[xf(x)]_{0}^{2}-\frac{3}{4}=2f(2)-\frac{3}{4}\] \[=\,\,\,0-\frac{3}{4}(\because f(2)=0)=-\frac{3}{4}.\]You need to login to perform this action.
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