Answer
True
Work Step by Step
Integration by parts should be used to evaluate this integral $\int^{1}_{0}xe^{10x}dx$
Let $u=x \rightarrow du=dx$
$dv=e^{10x}dx \rightarrow v=e^{10x}$
Then integrating by parts, we get:
$\int^{1}_{0}xe^{10x}dx=xe^{10x}|^{1}_{0}-\int^{1}_{0}e^{10x}dx=e^{10}-(\frac{e^{10x}}{10}|^{1}_{0})=\frac{9}{10}e^{10}-\frac{1}{10}$
