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Prove that underset(-a)overset(a)int f(x...

Prove that `underset(-a)overset(a)int f(x)dx={{:(,2underset(0)overset(a)int f(x)dx,"if f(x) is an even function"),(,0,"if f(x) is an odd function"):}` and hence evaluate `underset(-pi//2)overset(pi//2)int (x^(3)+x cos x)dx.`

Answer

Step by step text solution for Prove that underset(-a)overset(a)int f(x)dx={{:(,2underset(0)overset(a)int f(x)dx,"if f(x) is an even function"),(,0,"if f(x) is an odd function"):} and hence evaluate underset(-pi//2)overset(pi//2)int (x^(3)+x cos 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)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

Knowledge Check

  • underset(1)overset(e )int log x dx =

    A
    1
    B
    e-1
    C
    e+1
    D
    0

  • underset(0)overset(pi)intxf(sin x)dx=A underset(0)overset(pi//2)int f(sin x) dx then A is

    A
    0
    B
    `2pi`
    C
    `(pi)/(4)`
    D
    `pi`

  • underset(0)overset(pi//4)int log ((sin x+cos x)/(cos x))dx

    A
    a. log 2
    B
    b. `(pi)/(8)log 2`
    C
    c. `(pi)/(2)log 2`
    D
    d.`(pi)/(4) log 2`

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    Evaluate : underset(2)overset(3)int (xdx)/(x^(2)+1)

    The value of underset(0)overset(pi//2)int log tan x dx is

    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 .

    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 .

    underset(-pi//4)overset(pi//4)int (dx)/(1+cos 2x) is equal to

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