Question

Find the area bounded by the graphs of the indicated equations over the given interval.

1
y=e^x; y = --1/x ;0.5sxs
y=0.5≤x≤1

Answer 1

To find the area bounded by the graphs of the given equations, we need to find the points of intersection between the two curves. Once we have the x-values of intersection, we can set up the definite integral to calculate the area.

Step-by-step explanation:

To find the area bounded by the graphs of the given equations, we need to find the points of intersection between the two curves. The points of intersection will define the limits of integration for calculating the area.

First, let's find the points of intersection:

e^x = -1/x

Since these two equations cannot be solved analytically, we will need to use numerical methods or a graphing calculator to find the approximate x-values of intersection.

Once we have the x-values of intersection, we can set up the definite integral to calculate the area:

Area = ∫ (e^x - (-1/x)) dx from x = 0.5 to x = 1

We can evaluate this definite integral to find the area between the graphs over the given interval.