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Let f : R -> R and g : R -> R be contin...

Let `f : R -> R` and `g : R -> 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

`-1`

B

0

C

1

D

None of these

Text Solution

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The correct Answer is:
B
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise For Session 4
  1. Let f : R -> R and g : R -> R be continuous functions. Then the value...

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  2. The value of int(-1)^(1)(x|x|)dx is equal to

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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(x) is an odd function, then the value of int(-a)^(a)(f(sin x)/(f(...

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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. The value of int(-pi)^(pi)(cos^(2)x)/(1+a^(x)dx where agt 0, is

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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. The value of int(-pi//2)^(pi//2)(1)/(e^(sinx)+1) dx is equal to

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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. Let f(x)={(1-|x|","|x|le1),(0","|x|gt1):} and g(x)=f(x-1)"for all" x i...

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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 In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

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  19. If In=int-pi^pi (sinnx)/((1+pi^x)sinx)dx, n=0,1,2, …, then (A) In=I(n+...

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  20. If In=int-pi^pi (sinnx)/((1+pi^x)sinx)dx, n=0,1,2, …, then (A) In=I(n+...

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