Question

Find the area between the graph of the given function and the x-axis over the given interval, if possible.

f(x)=e-x, for [-[infinity], e]

Answer 1

Not possible to find out area

Explanation:

Given is an exponential function as

`f(x) =e^(-x)` and we have to find the area to the left of e above x axis under the curve.

Using integrals, we find area =

`\int\limits^e_(-\infty)  e^(-x)  \, dx\\=-e^(-x)`

substitute limits

When we substitute -infinity we get e^infty which is again infinity

Hence finding out area is not possible.

The integral of area diverges.