MCQ
The value of $\int \limits_{-2012}^{2012}\left(\sin \left(x^3\right)+x^5+1\right) d x$ is
- A$2012$
- B$2013$
- C$0$
- ✓$4024$
Let
$I =\int \limits_{-2012}^{2012}\left(\sin \left(x^3\right)+x^5+1\right) d x$
$\Rightarrow I =\int \limits_{-2012}^{2012} \sin x^3 d x+\int \limits_{-2012}^{2012} x^5 d x+\int \limits_{-2012}^{2012} d x$
$\Rightarrow I =0+0+2 \int \limits_0^{2012} d x$
$\Rightarrow I {\left[\because \sin x^3 \text { and } x^5 \text { are odd function }\right] }$
$=2[x]_0^{2012}=2 \times(2012)=4024$
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