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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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Knowledge Check

  • f: R rarr R, g: R rarr R are continuous functions. The value of integral int_(-pi//2)^(pi//2) [f(x) + f(-x)] [g(x) -g(-x)] dx is

    A
    `pi`
    B
    1
    C
    `-1`
    D
    0

  • If f and g are two continuous function, then the value of int_(-pi//4)^(pi//4){f(x)+f(-x)}{g(x)-g(-x)}dx is

    A
    `pi/4`
    B
    `0`
    C
    `-pi/4`
    D
    `pi`

  • Let f be a continuous function on R satisfying f(x+y)= f(x) + f(y) for all x, y in R with f(1) =2 and g be a function satisfying f(x) + g(x)= e^(x) then the value of the integral int_(0)^(1) f(x) g(x) dx is

    A
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