Hello sir, what the answer? Please help me

Question

If R is the region in the first quadrant bounded by x-axis, 2x+y=6 and y=2x, evaluate

∫ ∫_R 2ydA

Answer 1

it's a triangle with vertices (3/2, 3), (0,0) and (0,6)

it's area = bh/2 = 6(3/2)/2 = 9/2=4.5

just graph the lines and vertices

y=y

2x=-2x+6

4x=6

x=6/4=3/2

y=2x=2(3/2)=3

(3/2, 3)

that's one vertex

y=2x goes through the origin 2nd vertex (0, 0)

2x+y=6

y=-2x+6

(0, 6) is 3rd vertex