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Let y=f(x) satisfies the equation f(x)...

Let y=f(x) satisfies the equation
`f(x)=(e^(-e)+e^(x)) cosx-2x-int_(0)^(x)(x-t)f'(t)dt.`
The value of f'(0)+f''(0)equals to

A

`e^(-x)(cosx-sinx)+(e^(x))/(5)(3cos+sinx)+(2)/(5)e^(-x)`

B

`e^(-x)(cosx+sinx)+(e^(x))/(5)(3cos-sinx)-(2)/(5)e^(-x)`

C

`e^(-x)(cosx-sinx)+(e^(x))/(5)(3cos-sinx)+(2)/(5)e^(-x)`

D

`e^(-x)(cosx+sinx)+(e^(x))/(5)(3cos-sinx)-(2)/(5)e^(-x)`

Text Solution

Verified by Experts

The correct Answer is:
C
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