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Let f(x) be a function satisfying`f'(x)=f(x)` with`f(0) =1` and g(x) be a function that satisfies `f(x) + g(x) = x^2` . Then the value of the integral `int_0^1f(x) g(x) dx`, is

A

`1/4(e-7)`

B

`1/4(e-2)`

C

`1/2(e-3)`

D

`3-1/2e^(2)-3/2`

Text Solution

Verified by Experts

The correct Answer is:
D
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TARGET PUBLICATION-DEFINITE INTEGRALS-EVALUATIO TEST
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  14. If f(x)=Asin((pix)/2)+B, f'(1/2)=sqrt2 and int0^1 f(x)dx=(2A)/pi then ...

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  17. If for all real numbers y ,[y] is the greatest integer less than or eq...

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  18. Let f(x) = |{:(secx,cosx,sec^(2)x+cotx cosecx),(cos^(2)x,cos^(2)x,cose...

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  19. If (1)/(sqrt(a))underset(1)overset(a)int((3)/(2)sqrt(x)+1-(1)/(sqrt(x)...

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