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

Question

rulnick · Answer

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?

rulnick · Answer

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 ...

anonymous · Answer

to what?

rulnick · Answer

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

anonymous · Answer

Okay thanks

rulnick · Answer

welcome