7.2 definite integral — Maths STD 12 Science — Question

Let

$I =\int \limits_{-2012}^{2012}\left(\sin \left(x^3\right)+x^5+1\right) d x$

$\Rightarrow I =\int \limits_{-2012}^{2012} \sin x^3 d x+\int \limits_{-2012}^{2012} x^5 d x+\int \limits_{-2012}^{2012} d x$

$\Rightarrow I =0+0+2 \int \limits_0^{2012} d x$

$\Rightarrow I {\left[\because \sin x^3 \text { and } x^5 \text { are odd function }\right] }$

$=2[x]_0^{2012}=2 \times(2012)=4024$