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If f and g are continuous functions in [...

If f and g are continuous functions in [0, 1] satisfying `f(x) = f(a-x) and g(x) + g(a-x) = a`, then `int_(0)^(a)f(x)* g(x)dx` is equal to

A

`a/2`

B

`a/2int_(0)^(a)f(x)dx`

C

`int_(0)^(a)f(x)dx`

D

`aint_(0)^(a)f(x)dx`

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ACCURATE PUBLICATION-DEFINITE INTEGRALS-QUESTION CARRYING 1 MARK - TYPE-I
  1. int(0)^(pi)sin^(2)xcos^(3)dx is equal to

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  2. int0^pi sin^3xcos^5xdx is equal to :

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  3. int(0)^(pi//2)(sqrt(cosx)/(sqrt(sinx)+sqrt(cosx)))dx is equal to

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  4. int0^(pi/2) sin^(1/2x)/(sin^(1/2)x+cos^(1/2)x)dx is equal to :

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  5. int0^(pi/2) sin^(3/2x)/(sin^(3/2)x+cos^(3/2)x)dx is equal to :

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  6. int0^(pi/2) sin^(3/2x)/(sin^(3/2)x+cos^(3/2)x)dx is equal to :

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  7. int(0)^(pi//2)(sqrt(cosx)/(sqrt(sinx)+sqrt(cosx)))dx is equal to

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  8. int(0)^(2//3) (dx)/(4+9x^(2)) equals

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  9. The value of the integral int(1/3)^1 (x-x^3)^(1/3)/x^4 dx is :

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

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  11. The value of int(0)^(pi//2)log((4+3sinx)/(4+3cos x))dx is

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  12. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(2))dx is (are)

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  13. int(a+c)^(b+c)f(x)dx is equal to

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

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  15. If x=int(0)^(y)(dt)/sqrt(1+9t^(2)) and (d^(2)y)/(dx^(2))=ay, then a is...

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  16. int(-1)^(1)(x^(3)+abs(x)+1)/(x^(2)+2abs(x)+1)dx is equal to

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  17. If underset0 overset1 int e^t/(1+t)dt=a, then underset0 overset1 int(e...

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  18. int(-2)^(2)abs(xcospix)dx is equal to

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  19. int(-pi/4)^(pi/4)(dx)/(1+cos2x) is equal to

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  20. int(0)^(pi/2)sqrt(1-sin2x)dx is equal to

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