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Let `f: Rveca n dg: RvecR` be continuous function. Then the value of the integral `int_(-pi/2)^(pi/2)[f(x)+f(-x)][g(x)-g(-x)]dxi s` (a)`pi` (b) 1 (c) `-1` (d) 0

A

`pi`

B

1

C

-1

D

0

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Exercise
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  3. Let f: Rveca n dg: RvecR be continuous function. Then the value of the...

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  4. The value of int(-1//2)^(1//2) |xcos((pix)/(2))|dx is

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  5. The value of the integral int(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

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  6. The value of int(pi//2)^0 (1)/(9 cosx+12 sinx)dx is

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  7. If I=int(3)^(4) (1)/(3sqrt(logx))dxthen

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  8. If I=int(0)^(1//2) (1)/(sqrt(1-x^(2n)))dxthen which one of the follow...

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  9. Q. int0^pie^(cos^2x)( cos^3(2n+1) x dx, n in I

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  10. The value of the integral int(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal...

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  11. If int(0)^(1) (log(1+x)/(1+x^(2))dx=

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  12. Ifint(log2)^x(dx)/(sqrt(e^x-1))=pi/6,"then " x " is equal to" (a)4 ...

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  13. The value of the integral overset(pi)underset(0)int log(1+cos x)dx is

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  14. The value of the integral overset(pi)underset(0)int(1)/(a^(2)-2a cos x...

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  15. The integral int(0)^(pi//2) f(sin 2 x)sin x dx is equal to

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  16. int(0)^(pi) k(pix-x^(2))^(100)sin2x" dx" is equal to

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  17. The value of the integral int(2)^(4) (sqrt(x^(2)-4))/(x^(4))dx is

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

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  19. If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a n ...

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

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