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  4. The value of ∫ limits2-2(x cos x + sin x + 1)dx is

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Q. The value of $\int\limits^{2}_{-2}\left(x\, \cos\,x +\sin\,x + 1\right)dx$ is

WBJEEWBJEE 2011Integrals

Solution:

We know, if $f(x)$ is odd, then $\int\limits_{-a}^{a} f(x) d x=0$
$ \therefore I =\int\limits_{-2}^{2}(x \cos x+\sin x+1) d x $
$=0+0+\int\limits_{-2}^{2} d x $
$(\because x \cos x$ and $\sin x$ are odd)
$=[x]_{-2}^{2}=4$