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If int f(x) sin xcos x dx=(1)/(2(b^(2)-a...

If `int f(x) sin xcos x dx=(1)/(2(b^(2)-a^(2))``*(log f(x))+C`, where C is a costant of integration, then f(x)=

A

`(2)/((b^(2)-a^(2))sin2x)`

B

`(2)/(ab sin 2x)`

C

`(2)/((b^(2)-a^(2))cos 2x)`

D

`(1)/((b^(2)cos^(2)x+sin^(2)xa^(2))`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • if int f (x ) sin x cos x dx = (1)/(2(b^(2) -a^(2)) log f(x ) + c where C is a constant of intergration then f(x) =

    A
    `(2)/((b^(2) -a^(2)) sin 2 x)`
    B
    `(2)/(ab si n 2 x)`
    C
    `(2)/((b^(2)-a^(2) cos 2x)`
    D
    `(2 )/(ab cos 2 x)`

  • If f(x)sinx.cosxdx=(1)/(2(b^(2)-a^(2)))logf(x)+c , where c is the constant of integration, then f(x)=

    A
    `(2)/((b^(2)-a^(2))cos2x)`
    B
    `(2)/(abcos2x)`
    C
    `(2)/((b^(2)-a^(2))sin2x)`
    D
    `(2)/("ab"sin2x)`

  • if int xe^(2x) dx = e^(2x).f(x)+c , where c is the constant of integration, then f(x) is

    A
    (3x-1)/4
    B
    (2x+1)/2
    C
    (2x-1)/4
    D
    (x-4)/6

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