JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

I = \int \limits_{ - 1}^1 \,\,\left\{ {\left[ {{x^2}} \right]\,\, + \,\,\log \,\,\left( {\frac{{2 + x}}{{2 - x}}} \right)} \right\}dx

where

\left[ x \right]

denotes the greatest integer less than or equal to

x

, the

I

equals

View answer and explanation

Correct option: C

\mathrm{0}

The correct answer is C (0) because the integral simplifies to the integral of an even function plus the integral of an odd function, and the integral of the odd function over the symmetric interval is zero.

More Questions from DEFINITE INTEGRATION

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

is equal to If

f\left( x \right)

is differentiable and

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

, then

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

equals The value of

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

, where

[*]

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

equals If

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)

in terms of

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