_ - 1 ^1 ( x^2 + x )|x|dx = ......... - Vidyadip

MCQ

$\int\limits_{ - 1}^1 {\left( {{x^2} + x} \right)|x|dx = .........} $

A
$0$
✓
$\frac{1}{4}$
C
$1$
D
$2$

✓

Answer

Correct option: B.

$\frac{1}{4}$

$\int_{-1}^{1}(x^2+x)|x|dx$
$\int_{-1}^{1}x^2|x|dx+\int_{-1}^{1}x|x|dx$
અહી $\because\left(\int_{-1}^{1}x|x|dx=0 \right)$ એ અઉગ્મ વિધેય છે.
$=2\int_{0}^{1}x^2.xdx+0$
$=2\int_{0}^{1}x^3.dx$
$=2\left[\frac{x^4}{4}\right]_o^1$
$=2\left[(\frac{1}{4})-0\right]$
$\frac{1}{4}$

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