1. Find the are between the curves y=e^x and y=4-x^2 graphically.

Question

a.) set up the integral
b.) include bounds rounded to three decimal places
c.) use integral function on calculator

2. Find the area of the "triangular" region bounded by y=4-x on the left, y=sqrt(x-2) on the right and y=2 on the top. Set up the integral and use a calculator.

Answer 1

The curves intersect at x = -1.965 and x=1.058
so the area between the curves is
∫[-1.965,1.058] ((4-x^2)-e^x) dx

To do this using vertical strips of width dx involves changing boundaries at x=3. So instead, let's use horizontal strips of width dy, so we get
∫[1,2] ((y^2+2)-(4-y)) dy