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Prove that int(-a)^(a)f(x)dx= {(2int(0...

Prove that `int_(-a)^(a)f(x)dx= {(2int_(0)^(a)f(x)dx ,"if f(x) is even function"),(0, "if f(x) is odd function"):}` and hence evaluate `int_(-(pi)/(2))^((pi)/(2))sin^(7)xdx`

Text Solution

Verified by Experts

The correct Answer is:
`int_(-(pi)/(2))^((pi)/(2))sin^(7)xdx =0`
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Prove that int_(-a)^(a) dx = {(2int_(0)^(a) f(x) dx, if f(x) "is even"),(0, if f(x) "is odd"):} and hence evaluate (b) int_(-pi//2)^(pi//2) sin^(7) x dx .

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Knowledge Check

  • int_(-pi/2)^(pi/2) sin x. cosh x dx =

    A
    0
    B
    `pi/4`
    C
    `e^(pi)/4`
    D
    none of these

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