Evaluate $\displaystyle\int_{0}^{\infty }{x{{e}^{-4x}}\,\mathrm{d}x}$. Hence, find \(\displaystyle

Question

Evaluate $\displaystyle\int_{0}^{\infty }{x{{e}^{-4x}}\,\mathrm{d}x}$. Hence, find $\displaystyle\int_{0}^{\infty }{{{x}^{2}}{{e}^{-4x}}\,\mathrm{d}x}$.

Accepted Answer

(a) $\frac{1}{16}$ (b) $\frac{1}{32}$

Techniques of Integration - Integration by Parts

Techniques of Integration - Integration by Parts

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