A) \[\frac{f(x)}{g'(x)}\]
B) \[f'(x)g(x)-f(x)g'(x)\]
C) \[f(x)g'(x)-f'(x)g(x)\]
D) \[f(x)g'(x)+f'(x)g(x)\]
Correct Answer: C
Solution :
\[\int_{{}}^{{}}{[f(x)\,{g}''(x)-{f}''(x)\,g(x)]\,dx}\] \[=\int_{{}}^{{}}{f(x)\,{g}''(x)\,dx}-\int_{{}}^{{}}{{f}''(x)\,g(x)\,dx}\] \[=\left( f(x)\,{g}'(x)-\int_{{}}^{{}}{{f}'(x){g}'(x)\,dx} \right)-\left( g(x)\,{f}'(x)-\int_{{}}^{{}}{{g}'(x)\,{f}'(x)\,dx} \right)\] \[=f(x)\,{g}'(x)-{f}'(x)\,g(x).\]You need to login to perform this action.
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