Find the area

Question

Find the area of the region bounded by the graphs of y = x, y = 4 - 3x, and x = 0.

Answer 1

This area is a triangle with the base along the y-axis from y=0 to y=4.

The altitude is the distance of the intersection of the lines y=x and y=4-3x, the point (1,1), from the y-axis

namely 1.  The area is 4×1/2=2.

If you absolutely need to use calculus

Area is ∫₀¹(4-4x)dx=2