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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

If

\int\limits_{0}^\pi x f\left(\cos ^2 x+\tan ^4 x\right) d x=k \int\limits_{0}^{\pi / 2} f\left(\cos ^2 x+\tan ^4 x\right) d x

, then the value of

k

is

View answer and explanation

Correct option: B

\pi

Option B (

\pi

) is correct because, after applying the definite integral property and simplification, the value of k is found to be

\pi

.

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f\left( {\frac{4}{{25}}} \right)

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\int\limits_{{0}}^{11}[x]^{3} . \mathrm{dx}

[*]

denotes the greatest integer function, is The integral

\int\limits_{2}^4 \frac{\log x^2}{\log x^2+\log \left(36-12 x+x^2\right)} d x

is equal to: The definite integral

\int\limits_{{-2}}^0\left(x^3+3 x^2+3 x+3+(x+1) \cos (x+1)\right) d x

I\,\,\left( {m,\,\,n} \right) = \int \nolimits_0^1 \,\,{t^m}\,\,{\left( {1 + t} \right)^n}\,\,dt

,then the expression for

I\left( {m,\,\,n} \right)

I\,\,\left( {m + 1,\,\,n + 1} \right)