The value of the integral $\mathop \smallint \limits_a^b \,\,\frac{{\left| {\,x\,} \right|}}{x}\,\,dx,\,\;a < b$ is

$\left| {\,a\,} \right|\,\, - \,\,\left| {\,b\,} \right|$

$\left| {\,a\,} \right|\,\, - \,\,b$

$\left| {\,b\,} \right|\,\, - \,\,a$

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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of the integral

\int \limits_a^b \,\,\frac{{\left| {\,x\,} \right|}}{x}\,\,dx,\,\;a < b

View answer and explanation

Correct option: B

\left| {\,b\,} \right|\,\, - \,\,\left| {\,a\,} \right|

Option B (

\left| {\,b\} \right|\, - \,\left| {\,a\} \right|

) is correct because the integral of |x|/x from a to b, where a < b, always results in the absolute value of b minus the absolute value of a, regardless of the signs of a and b.

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

[*]

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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

,then the expression for

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

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