Question

If $\int_{}^{}{g(x)dx}$= g(x), then $\int_{}^{}{g(x)\{ f(x) + f'(x)\} dx}$is equal to-

• A. g(x) f(x) – g(x) f ¢(x) + c
• B. g(x) f ¢(x) + c
• C. g(x) f(x) + c
• D. g(x) f² (x) + c

Answer 1

Answer: (C)

g(x) f(x) + c

Answer 2

I = $\int \mathrm { g } ( \mathrm { x } ) \left\{ \mathrm { f } ( \mathrm { x } ) + \mathrm { f } ^ { \prime } ( \mathrm { x } ) \right\} \mathrm { dx }$ using ILATE, we get

I = f(x) – $\int \left( f ^ { \prime } ( x ) \cdot \int g ( x ) d x \right)$dx

+

I = f(x) g(x) –+

I = f(x) g(x) + c