Mathematics · University
Integrate a decaying exponential · formula reference
Convergence requires k > 0. The upper limit is a limit, not a substitution of a finite number.
Formula
Convergence requires k > 0. The upper limit is a limit, not a substitution of a finite number.
∫₀∞ A exp(−kx) dx = A/k
Worked example
Evaluate the improper integral from 0 to infinity of 18 exp(−9x) dx. Round the final result to 4 decimal places if needed.
An antiderivative is −(18/9)exp(−9x). Its limit at infinity is zero. Subtract its value at zero.
2
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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