A) -1
B) 0
C) 1
D) \[\pi \]
Correct Answer: B
Solution :
Let \[l=\int_{0}^{\pi }{{{e}^{{{\sin }^{2}}x}}{{\cos }^{3}}xdx}\] ? (i) \[\Rightarrow \] \[l=\int_{0}^{\pi }{{{e}^{{{\sin }^{2}}(\pi -x)}}{{\cos }^{3}}(\pi -x)}dx\] \[\left[ \because \int_{0}^{a}{f(x)dx=\int_{0}^{a}{f(a-x)}dx} \right]\] \[\Rightarrow \] \[l=-\int_{0}^{\pi }{{{e}^{{{\sin }^{2}}x}}{{\cos }^{\text{3}}}x\text{ }dx}\] ? (i) On adding Eqs. (i) and (ii), we get \[2l=0\Rightarrow l=0\]
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