Definite Integral of Exponential Functions


$$ \begin{align} \displaystyle
\int_{n}^{m}{e^{ax+b}}dx &= \dfrac{1}{a}\big[e^{ax+b}\big]_{n}^{m} \\
&= \dfrac{1}{a}\big[e^{am+b}-e^{an+b}\big] \\
\end{align} $$

Example 1

Find $\displaystyle \int_{2}^{4}{e^{2x-4}}dx$, leaving the answer in exact form.

Example 2

Find $\displaystyle \int_{0}^{1}{(e^x+1)^2}dx$.

Example 3

Find $\displaystyle \int_{0}^{4}{\dfrac{1}{e^x}}dx$.

Example 4

Find $\displaystyle \int_{1}^{4}{e^{1-x}}dx$.






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