A) \[\frac{1}{2}{{f}^{2}}(x)\]
B) \[\frac{1}{2}{{g}^{2}}(x)\]
C) \[\frac{1}{2}{{[g'(x)]}^{2}}\]
D) \[f'(x)g(x)\]
Correct Answer: B
Solution :
Given, \[\int{f(x)}dx=g(x)\] \[\therefore \] \[\int{f\underset{II}{\mathop{(x)}}\,}g\underset{I}{\mathop{(x)}}\,dx=g(x)\int{f(x)\,dx}\] \[-\int{[g'(x)\int{f(x)dx]dx}}\] \[=g(x)g(x)-\int{g'(x)g(x)dx}\] \[={{[g(x)]}^{2}}-\frac{[g{{(x)}^{2}}]}{2}\] \[=\frac{{{g}^{2}}(x)}{2}\]You need to login to perform this action.
You will be redirected in
3 sec