A) \[\pi \]
B) 1
C) 0
D) None of these
Correct Answer: D
Solution :
Let\[I=\int_{0}^{\pi }{{{e}^{{{\cos }^{2}}x}}}.{{\cos }^{3}}(2n+1)xdx\]Using \[\int_{0}^{a}{f(x)dx}\left\{ \begin{align} & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0,f(a-x)=-f(x) \\ & 2\int_{0}^{a/2}{f(x)dx,f(a-x)=f(x)} \\ \end{align} \right.\] where, \[f(x)={{e}^{{{\cos }^{2}}x}}.{{\cos }^{3}}(2n+1)x\] Now, \[f(\pi -x)=({{e}^{{{\cos }^{2}}x}})[-{{\cos }^{3}}(2n+1)x]\] \[=-f(x)\] \[\therefore \]\[I=0\]
You need to login to perform this action.
You will be redirected in
3 sec
