Question

Find the area of the region bounded by the graphs of y = x, y = 6 - 2x, and y = 0. (4 points)

3
6
9
None of these

Please help I don't know how to do this

Answer 1

intersection of y = x and y = 6-2x
x = 6-2x
3x = 6
x = 2 , so y = 2

so you have a triangle with vertices
(0,0), (2,2) and ((3,0), the last one is the x-intercept.

Surely you don't Calculus to do this.
base = 3, height = 2
Area = (1/2)(3)(2) = 3

Answer 2

However, if you want to exercise your calculus, you can do it as

vertical strips:

∫[0,2] x dx + ∫[2,3] 6-2x dx = 2+1 = 3

or as horizontal strips:
∫[0,2] (3 - y/2)-y dy = 3