Mathematics · University
Integrate a decaying exponential
Convergence requires k > 0. The upper limit is a limit, not a substitution of a finite number.
Method and conditions
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 examples
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
Evaluate the improper integral from 0 to infinity of 25 exp(−3x) dx. Round the final result to 4 decimal places if needed.
An antiderivative is −(25/3)exp(−3x). Its limit at infinity is zero. Subtract its value at zero.
8.3333
Try it
Evaluate the improper integral from 0 to infinity of 32 exp(−2x) dx. Round the final result to 4 decimal places if needed.
Evaluate the improper integral from 0 to infinity of 3 exp(−8x) dx. Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 16
An antiderivative is −(32/2)exp(−2x). Its limit at infinity is zero. Subtract its value at zero.
- 0.375
An antiderivative is −(3/8)exp(−8x). Its limit at infinity is zero. Subtract its value at zero.
Further reading and review references
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