find the area of region R bounded by the curves y=3x , x=2y and 2x+y=5

Answer 1

You need to divide the region into two parts at x=1, where 3x and 5-2x intersect.

a = ∫[0,1] (3x - x/2) dx + ∫[1,2] (5-2x - x/2) dx

See the region at

http://www.wolframalpha.com/input/?i=plot+y%3D3x%2Cy%3Dx%2F2%2Cy%3D5-2x