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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

`-1`

B

0

C

1

D

None of these

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The correct Answer is:
B
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ARIHANT MATHS ENGLISH-DEFINITE INTEGRAL-Exercise For Session 4
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  3. The value of int(-1)^(1)((x^(2)+ sin x)/(1+x^(2)))dx is equal to

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  4. If f is an odd function, then evaluate I=int(-a)^a(f(sinx)dx)/(f(cosx...

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  5. Evaluate: int-(1/sqrt(3))^(1/sqrt(3)) (cos^-1((2x)/(1+x^2))+tan^-1((2x...

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  6. Find the value of int(-pi)^(pi)(cos^(2)x)/(1+a^(x))dx, agt0.

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  7. The integral int(-1/2)^(1/2) ([x]+1n((1+x)/(1-x)))dx is equal to (wher...

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  8. Evaluate: int(-pi//2)^(pi//2)1/(1+e^(sin x))dx

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  9. If [*] denots the greatest integer function then the value of the inte...

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  10. The equation int(-pi/4)^(pi/4){a|sinx|+(bsinx)/(1+cos^2x)+c}dx=0 where...

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  11. The value of int(-2)^(2)(sin^(2)x)/([(x)/(pi)]+(1)/(2))dx where [.] d...

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  12. Let f(x) be a contiuous function such a intn^(n+1) f(x)dx=n^3, n in Z...

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  13. Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...

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  14. Let f: R rarr R be a continuous function given by f(x+y)=f(x)+f(y) for...

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  15. The value of int(-2)^(2) |[x]| dx is equal to

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  16. Find the second order derivative if y= e^(2x)

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  17. Let f(x)={1-|x|,|x| leq 1 and 0,|x| lt 1 and g(x)=f(x-)+f(x + 1), for...

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  18. If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then

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  19. If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then

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  20. If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then

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