Problem

Find the area bounded by the graphs of the indicated equations over the given interval. \[ y=e^{0.5 x} ; y=-\frac{1}{x} ; 1 \leq x \leq 2 \] The area is $\square$ square units. (Type an integer or decimal rounded to three decimal places as needed.)

Solution

Step 1 :First, we define the two functions \(y=e^{0.5 x}\) and \(y=-\frac{1}{x}\).

Step 2 :Next, we define the absolute difference function which is the absolute value of the difference between the two functions.

Step 3 :Then, we perform numerical integration on the absolute difference function over the interval from 1 to 2.

Step 4 :After running the numerical integration, we get the numerical value of the area bounded by the two functions over the interval [1, 2].

Step 5 :Finally, the area bounded by the graphs of the indicated equations over the given interval is \(\boxed{area}\) square units.

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Source: https://solvelyapp.com/problems/diS6cVbmfb/

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