JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Statement-I :

\int e^x \sin x d x=\frac{e^x}{2}(\sin x-\cos x)+c

.

Statement-II :

\int e^x\left(f(x)+f^{\prime}(x)\right) d x=e^x f(x)+c

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Correct option: A

If both Statement - I and Statement - II are true, and Statement - II is the correct explanation of Statement- I.

Option A is correct because both statements are true, and Statement II correctly explains Statement I, as Statement I is a specific case of Statement II.

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\int \nolimits_0^\infty \,\,\log \,\,\left( {x + \frac{1}{x}} \right)\,\,\frac{{dx}}{{1 + {x^2}}}

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f\left( x \right)

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\int \nolimits_0^{{t^2}} \,\,x\;\,f\left( x \right)\,\,dx = \frac{2}{5}\,\,{t^5}

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

equals The value of

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

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[*]

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

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

equals If

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

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

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