definite Integral.. (3 may)

\hspace{-16}\bf{\int_{-1}^{1}\frac{2x^{1004}+x^{3014}+x^{2008}.\sin(x)^{2007}}{1+x^{2010}}dx}

1 Answers

1
rishabh ·

since sin is odd function,

\begin{align*} & \mathbb{I} = 2\int_{0}^{1} \frac{x^{1004}}{1+x^{2010}} + x^{1004} \\ &= 2[ \frac{\tan ^{-1}(x^{1005})}{1005} +\frac{x^{1005}}{1005} ]\\ &= \frac{2}{1005}[\frac{\pi}{4}+1] \\ & \bullet \bullet \bullet \bullet \\ & \\ & \\ & \\ & \\ & \\ & \end{align*}

Your Answer

Close [X]