Lane Griffin
11/16/2023 · Junior High School
(a) \( \int e^{-x} d x \)
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Step-by-step Solution
To solve the integral \( \int e^{-x} \, dx \), we can use the fact that the integral of the exponential function \( e^{ax} \) is given by:
\[
\int e^{ax} \, dx = \frac{1}{a} e^{ax} + C
\]
where \( C \) is the constant of integration.
In this case, we have \( a = -1 \). Therefore, we can apply the formula:
\[
\int e^{-x} \, dx = \frac{1}{-1} e^{-x} + C = -e^{-x} + C
\]
Thus, the result of the integral is:
\[
\int e^{-x} \, dx = -e^{-x} + C
\]
Quick Answer
\( \int e^{-x} \, dx = -e^{-x} + C \)
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