MCQ
$\int_{\,0}^{\,\pi } {{e^{{{\sin }^2}x}}{{\cos }^3}x\,dx} $ is equals to
- A$ - 1$
- ✓$0$
- C$1$
- D$\pi $
$ \Rightarrow I = \int_0^\pi {{e^{{{\sin }^2}(\pi - x)}}{{\cos }^3}(\pi - x)\,} dx$ ..$(i)$
$ \Rightarrow I = - \int_0^\pi {{e^{{{\sin }^2}x}}{{\cos }^3}x\,dx} $ ..$(ii)$
Adding $(i)$ and $(ii),$ we get
$2I = 0$ ==> $I = 0$.
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