The value of $\mathop \smallint \limits_\alpha ^\beta \,x\,\;\left| {\,x\,} \right|\,\,dx$, where $\alpha < 0 < \beta $, is

$\frac{1}{2}\,\,\left( {{\alpha ^2} + {\beta ^2}} \right)$

$\frac{1}{3}\,\,\left( {{\beta ^2} - {\alpha ^2}} \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of

\int \limits_\alpha ^\beta \,x\,\;\left| {\,x\,} \right|\,\,dx

, where

\alpha < 0 < \beta

, is

View answer and explanation

Correct option: C

\frac{1}{3}\,\,\left( {{\alpha ^3} + {\beta ^3}} \right)

Option D (None of these) is incorrect; the correct answer is

\frac{1}{3}\,\,\left( {{\alpha ^3} + {\beta ^3}} \right)

, derived by splitting the integral and considering the absolute value.

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