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If fa n dg are continuous function on [0...

If `fa n dg` are continuous function on `[0,a]` satisfying `f(x)=f(a-x)a n dg(x)(a-x)=2,` then show that `int_0^af(x)g(x)dx=int_0^af(x)dxdot`

A

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

B

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

C

0

D

none of these

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-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 fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a n ...

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

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  5. Choose the correct answer The value of the integral int1/3 1((x-x^3)^(...

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  6. Evaluate: int0^(100pi)sqrt((1-cos2x))dxdot

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  7. Evaluate: int(-1/2)^(1/2)[((x+1)/(x-1))^2+((x-1)/(x+1))^2-2]^(1/2)dx

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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. T h ev a l u eofint0^(pi/2)(dx)/(1+tan^3x)i s 0 (b) 1 (c) pi/2 (d...

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  12. The value of int0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >...

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  13. If (d(f(x)))/(dx) = g(x) AA x in [a, b] then int(a)^(b)f(x).g(x)dx is ...

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  14. For any integer n,the integral overset(pi)underset(0)int e^(sin^(2)x)c...

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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)xdx, 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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