Resources for Applications of Integration e^x
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Questions
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Applications of Integration e^x Theory
![Applications of the integration of exponential functions involves determining areas and the use of the trapezoidal rule.\\ \begin{multicols}{2} \textbf{Example 1}\\ %10641 Find the area bounded by the curve \(y = {e^x} + 1\) the \(x\)-axis and the lines \(x=1\) and \(x=2\)\\ \textbf{Example 1 solution}\\ $\begin{aligned} \text { Area }&=\int_{1}^{2} e^{x}+1 d x\\ &=\left[e^{x}+x\right]_{1}^{2} \\ &=\left[\left(e^{2}+2\right)-(e+1)\right] \\ &=(e^{2}-e+1) u^{2} \end{aligned}$\\ \columnbreak \textbf{Example 2}\\ %10639 Use the trapezoidal rule and 3 function values to approximate the area bounded by \(y = {e^{{x^2} + 1}}\) the x - axis and \(x = 0\), \(x = 2\)\\ \textbf{Example 2 solution}\\ $\begin{aligned} \text { Area } &=\frac{1}{2}[f(0)+2 f(1)+f(2)] \\ &=\frac{1}{2}\left[e+2 e^{2}+e^{5}\right] \\ & = 82 . 95 \end{aligned}$\\ \end{multicols}](/media/bdihgely/4782.png)