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Let f:R to R be continuous functions. Th...

Let `f:R to R` be continuous functions. Then the value of the integral `int_(-pi//2)^(pi//2) [f(x)+f(-x)][g(x)-g(-x)]dx` is

A

`pi`

B

1

C

-1

D

0

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The correct Answer is:
D
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. If f(x)=f(a+b-x) for all x in[a,b] and int(a)^(b) xf(x) dx=k int(a)^(b...

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  2. To find the numberical value of int(-2)^(2) (px^(3)+qx+8)dx it is nece...

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  3. Let f:R to R be continuous functions. Then the value of the integral i...

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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. If I=int(0)^(1//2) (sin^(2)n x)/(sin^(2)x)dxthen which one of the foll...

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  10. For any integer n, the integral int0^pie^(cosx)cos^3(2n+1)xdx has the ...

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

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  12. If int(0)^(oo) (log(1+x^(2)))/(1+x^(2))dx=kint(0)^(oo) (log(1+x))/(1+x...

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  13. If int(log2)^(x) (1)/(sqrt(e^(x)-1))dx=(pi)/(6)then x is equal to

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

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  15. The integral int(0)^(pi) (1)/(a^(2)-2 a cos x+1)dx (a lt 1) is

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

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

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

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

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

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