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If f(pi) = 2 and int0^(pi) [f(x)+f^('')(...

If `f(pi) = 2` and `int_0^(pi) [f(x)+f^('')(x)] sin x dx = 5` then f(0)

A

7

B

3

C

5

D

1

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The correct Answer is:
B
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. Let f : [1, oo) rarr [2, oo) be a differentiable function such that f(...

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  2. The critical point of : f(x) = 1 + x + int1^x [(log t)^2 + 2 log t] ...

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  3. If f(pi) = 2 and int0^(pi) [f(x)+f^('')(x)] sin x dx = 5 then f(0)

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  4. int(-1)^(1) d/(dx) (1/(1+e^(1/x))) dx =

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  5. inta^(b) f(x) dx is equal to

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  6. If f and g are continuous functions in [0,1] satisfying f(x) = f(a - x...

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  7. If x=int0^(y) (dt)/(sqrt(1+9t^(2))) and (d^(2)y)/(dx^(2)) = ay, then a...

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  8. int(-1)^(1) (x^3 + |x| + 1)/(x^2 + 2|x| + 1) dx is equal to :

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  9. If int0^1 (e^t)/(1 + t) dt = a, then int0^1 (e^t)/((1 + t)^(2))dt is e...

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  10. int(-2)^2 |x cos pi x|dx is equal to :

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  11. int(-pi//4)^(pi//4)(dx)/(1+cos 2x) is equal to

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  12. int(0)^(pi//4) sqrt(1 -sin 2x dx) is equal to :

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  13. Choose the correct answer int(1)^(sqrt3)(dx)/(1+x^(2)) equals

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  14. Choose the correct answer int(0)^(2/3)(dx)/(4+9x^(2)) equals

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  15. If f(x) = int(0)^(x) t sin t dt, then f'(x) is

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  16. Choose the correct answer The value of the integral int(1/3)^(1)((x-...

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  17. Choose the correct answer The value of int((-pi)/2)^(pi/2)(x^(3)+xco...

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  18. The value of int0^(pi/2) log ((4+3sinx)/(4+3cosx)) dx is

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  19. If f(a + b - x) = fx, then inta^b x f(x) dx is equal to :

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  20. The value of int0^(1) tan^(-1) ((2x-1)/(1+x-x^(2))) dx is

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