Evaluate
\frac{t^{2}}{e^{500t}}
Differentiate w.r.t. t
\frac{2t\left(1-250t\right)}{e^{500t}}
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\int \frac{t}{e^{500t}}\mathrm{d}x
Evaluate the indefinite integral first.
\frac{t}{e^{500t}}x
Find the integral of \frac{t}{e^{500t}} using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{tx}{e^{500t}}
Simplify.
te^{-500t}t-te^{-500t}\times 0
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
\frac{t^{2}}{e^{500t}}
Simplify.
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