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If f(x) and g(x) are continuous functions satisfying `(x)=f(a-x) and g(x)+g(a-x)=2, then
`int_(0)^(a) f(x) g(x) dx` is equal to

A

`overset(a)underset(0)int g(x) dx`

B

`overset(a)underset(0)int f(x) dx`

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. The value of the integral int(2)^(4) (sqrt(x^(2)-4))/(x^(4))dx is

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  2. The value of the integral int(0)^(pi)(1)/(a^(2)-2a cos x+1)dx (a gt1),...

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  3. If f(x) and g(x) are continuous functions satisfying (x)=f(a-x) and g(...

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  4. int0^(pi//2) x(sqrt(tan x)+sqrt(cot x))dx equals

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

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  6. The value of the integral int(0)^(100pi) sqrt(1-cos2x)" d"xis

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  7. The value of the integral int(-1//2)^(1//2) {((x+1)/(x-1))^(2)+((x-...

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  8. The value of the integral int(1//e)^(e) |logx|dx, is

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  9. The value of int(0)^(pi//2) (sin 8x log cot x)/(cos 2x)dx, is

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  10. The value of int(0)^(pi//2) x^(10) sin x" dx", is then the value of m...

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  11. The value of int(0)^(pi//2) (1)/(1+tan^(3)x)dx is

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  12. The value of int0^pi(sin(n+1/2)x)/(sin(x/2)dx is

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  13. If (d)/(dx)f(x)=g(x) for a le x le b then, int(a)^(b) f(x) g(x) dx eq...

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  14. For any integer n,the integral int(0)^(3) e^(sin^(2)x)cos^(3)(2n+1)x" ...

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  15. The value of the integral int(0)^(3) sqrt(3+x^(3))dxlies in the inter...

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  16. The value of the integral int(0)^(1) (1)/((1+x^(2))^(3//2))dx is

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  17. If I=int(0)^(2pi) sin^(2) x" dx", then

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  18. If int(0)^(1) f(x)=M,int(0)^(1) g(x)dx=N, then which of the following ...

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  19. The value of int( 0)^(pi//4) (pix-4x^(2))log(1+tanx)dx is

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  20. The value of int(-pi//2)^(pi//2) sin{log(x+sqrt(x^(2)+1)}dx is

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