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Let inte^x{f(x)-f^(prime)(x)}dx=varphi(x...

Let `inte^x{f(x)-f^(prime)(x)}dx=varphi(x)dot` Then `inte^xf(x)dx` is `varphi(x)=`e^xf(x)

A

`phi(x)=e^(x)f(x)`

B

`phi(x)-e^(x)f(x)`

C

`(1)/(2){phi(x)+e^(x)f(x)}`

D

`(1)/(2){phi(x)+e^(x)f'(x)}`

Text Solution

Verified by Experts

The correct Answer is:
C
Here, `int e^(x){f(x)-f'(x)}dx=phi(x)`
and `int e^(x){f(x)+f'(x)}dx=e^(x)f(x)`
On adding, we get `2int e^(x)f(x)dx=phi(x)+e^(x)f(x)`
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