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If f(0) = 1, f(2) = 3, f'(2) = 5 and f'(...

If `f(0) = 1, f(2) = 3, f'(2) = 5 and f'(0)` is finite, then `int_0^1 xf''(2x) dx` is equal to (A) zero (B) 1 (C)2 (D) none of these

A

zero

B

1

C

2

D

None of these

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The correct Answer is:
C
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. If int1^x (dt)/(|t|sqrt(t^2-1))=pi/6 then x can be equal to

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  2. int (0) ^(pi//4) ( sin x )/( cos ^(3) x) dx equal to :

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  3. If f(0) = 1, f(2) = 3, f'(2) = 5 and f'(0) is finite, then int0^1 xf''...

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  4. If I (1) = int (e) ^(e ^(2)) (dx )/( ln x ) and I (2) = int (1) ^(2) (...

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  5. int (0) ^((pi//2)^(1//3)) x ^(5). sin x ^(3) dx equal to

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  6. If A=int(0)^(pi)cosx/(x+2)^2.dx, then int(0)^(pi/2)sin(2x)/(x+1).dx i...

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  7. If f(x)={0 ,where x=n/(n+1), n =1, 2, 3.... and 1 , else w...

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  8. If f(pi)=2 and int(0)^(pi)(f(x)+f''(x))sin x dx=5, then f(0) is equal ...

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

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  10. int (0) ^(2) (x - log (2) a ) dx =2 log (2) ((2)/(a)), if

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  11. If overset(x)underset(log2)int (1)/(sqrt(e^(x)-1))dx=(pi)/(6)then x is...

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  12. If f(x) is a continuous function and attains only rational values in [...

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

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

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

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

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

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

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

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