Question

What is the definite integral of this e^|x| . limit is from -2 to +8?

Answer 1

Answer on question #51702 | Math, Integral Calculus

What is the definite integral of this $e^{\wedge}|x|$ . limit is from -2 to +8?

Solution

$$\begin{array}{l} \int_{-2}^{8} e^{[x]} dx = \int_{-2}^{0} e^{-x} dx + \int_{0}^{8} e^{x} dx = - \int_{-2}^{0} e^{-x} d(-x) + \int_{0}^{8} e^{x} dx = - e^{-x} \left| \begin{array}{c} 0 \\ -2 \end{array} \right. + e^{x} \left| \begin{array}{c} 8 \\ 0 \end{array} \right. = \\ = -1 + e^{2} + e^{8} - 1 = e^{8} + e^{2} - 2 \\ \end{array}$$

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