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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

`e = (e ^(2))/( 2) + 5/2`

B

`e - (e ^(2))/(2) - 5/2`

C

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

D

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

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The correct Answer is:
D
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. If f(x) is a continuous function and attains only rational values in [...

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  2. If f(y)=e^(y), g(y)=y, y gt 0 and F(t)=int(0)^(t) f(t-y)g(y)dy, then ...

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  3. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

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  4. int(0) ^(pi//2) ((sin x +cos x )^(2))/sqrt(1+ sin 2x)dx =

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  5. int (0) ^(pi//4) sin (x- [x])d (x-[x]) is equal to

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  6. For 0 lt x lt pi/2, int (1//sqrt2) ^(1//2) cot x s (cos x ) equal to

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  7. The value of int (pi//4) ^(pi//3) cosec x d (sin x ) for 0 lt x lt pi...

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  8. Find the value of : int0^(10)e^(2x-[2x])d(x-[x])w h e r e[dot] denote...

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  9. int (log pi - log 2 ) ^(log pi) (e ^(x))/(1- cos ((2)/(3)e ^(x)))dx i...

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  10. If underset(0)overset(oo)int e^(-x^(2))dx=sqrt((pi)/(2))"then"underset...

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  11. Let A = underset(0)overset(1)int(e^(t))/(1+t) dt, then underset(a-1)ov...

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  12. Let (d)/(dx) F(x)=(e^(sin x))/(x), x gt 0, If int(1)^(4) (3)/(x) ...

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  13. 1/c int (a) ^(b) f ((x)/(c )) dx =

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  14. int(5/2)^5 (sqrt((25-x^2)^3))/(x^4) dx

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  15. If {:(f(x)=x", ...."x lt 1),(" "=x-1", ...." x ge 1","):} ...

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  16. Suppose for every integer n, . underset(n)overset(n+1)intf(x)dx = n^(2...

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  17. int (0) ^(pi) (1 + 2 cos x ) dx equal to :

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  18. The value of int (-1) ^(3) (|x-2 |+[x]) dx is equal to (where [**] den...

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  19. If underset(-1)overset(3//2)int|xsinpix|dx = (k)/(pi^(2)), then the va...

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  20. int0^(10pi) |sin x| dx is

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