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

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`.

Answer

Step by step text solution for 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. by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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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 (d) int_(-pi//2)^(pi//2)tan^(9) xdx .

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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
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  • int_(-pi/2)^(pi/2) cos x. sinh x dx =

    A
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    B
    `e^(pi)`
    C
    0
    D
    `-pi/4`

  • int_(0)^(pi//2)x sin^2 x dx=

    A
    `pi^2/4 + 1/16`
    B
    `pi^2/16 + 1/4`
    C
    `pi^2`
    D
    0

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