Question

Find the area between the curves on the given interval. y = ex, y = x – 1, -2 ≤ x ≤ 0

Answer 1

It is always a good idea to sketch first. If you do, you will see that x-1 is below the x axis everywhere on the interval -2 <= x <= 0, and of course e^x is above it. So the integrals may be computed separately if convenient. And just to confirm, it is "e to the x power" right?

Answer 2

This definite integral of e^x is 1-e^-2.
And for x-1 it is -4.
The difference is then 1-e^-2-(-4), which simplifies to ...

Answer 3

to what?

Answer 4

The constant terms can be combined, so it simplifies to 5-e^-2. And this difference is the area between the two curves.

Answer 5

Okay thanks

Answer 6

welcome