Calculus
posted by Alex .
Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer.
Between y = −x and y = x/2 for x in [0, 6]

Did you follow suggestion and sketch the lines?
I see a triangle with vertices
(0,0), (6,3) and (6,6)
You certainly would not need Calculus for this
base = 9, height = 6
area = (1/2)(9)(6) = 27
If you have to use Calculus ....
effective height = x/2  (x) = (3/2)x
area = ∫(3/2) x dx from 0 to 6
= (3/4)x^2  from 0 to 6
= (3/4)(36)  0 = 27