R is the first quadrant region enclosed by the x-axis, the curve y = 2x + b, and the line x = b, where b > 0. Find the value of b so that the area of the region R is 288 square units.

Answer 1

simple enough. You want

∫[0,b] (2x+b) dx = 288

Now just solve for b. You can check by just finding the area of the trapezoid:

b(b + 2b+b)/2 = 288

Answer 2

Answer is 12