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If f(a + b - x) = fx, then inta^b x f(x)...

If `f(a + b - x) = fx`, then `int_a^b x f(x) dx` is equal to :

A

`(a+b)/2 int_a^(b) f(x) dx`

B

`(b-a)/2 int_a^(b) f(x) dx`

C

`(a+b)/2 int_a^(b) f(a+b-x) dx`

D

`(a+b)/2 int_a^(b) f(b-x) dx`

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The correct Answer is:
A
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
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  3. If f(a + b - x) = fx, then inta^b x f(x) dx is equal to :

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  4. The value of the integral I = int0^1 x (1 - x)^(n) dx is :

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  5. Let d/(dx) F(x) = ((e^(sin x))/(x)) , x > 0. If int1^4 3/x e^(sin x^3)...

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  7. Let f(x) be a function satisfying f'(x) = f(x) with f(0) = 1 and g(x) ...

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  8. If f(x) = (e^x)/(1 + e^x) , I1 = int(f(-a))^(f(a)) x g {x(1 - x)} dx a...

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  9. The value of I = int0^(pi//2) ((sin x + cos x)^2)/(sqrt(1 + sin 2x)) d...

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  10. The value of int(-2)^3 |1 - x^2| dx is:

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  11. If int0^pi x f (sin x)dx = A int0^(pi//2) f (sin x) dx, then A is :

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  12. Let F : R to R be a differentiable function having : f(2) = 6, f'(2) =...

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  13. int0^(pi) x f (sin x) dx is equal to :

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  14. int(-3pi//2)^(-pi//2) [(x +pi)^3 + cos^2 (x + 3x)]dx is equal to :

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  15. If f(x) ={(e^(cosx)sinx; |x| le 2),(2 ; othe...

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  16. The value of integral int(e^(-1))^(e^2) |(loge x)/(x)| dx is :

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  17. Let g(x) = int0^(x) f(t) dt, where 1/2 le f(t) < 1, t in [0,1] and 0 <...

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  18. The value of int(-pi)^(pi) (cos^2 x)/(1 + a^x) dx, a > 0, is :

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  19. Let f : (0, oo ) to R and F(x) = int0^x f(t) dt. If F(x^2) = x^2(1 +...

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  20. Let f(x) = int1^x sqrt(2 - t^2) dt. Then the real roots of the equatio...

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