Find the area of the region bounded by the three lines below. [Hint: You will have to split up the integral into two parts.]

Question

y=4/3x, y=7x, y=3/2x +17/2

Answer 1

As Doug has demonstrated the graph is a triangle.

In addition to what Doug has suggested, there is another method for finding the area of a triangle given the co-ordinates of its vertices.

In this case it is particularly easy since one of the vertices is (0,0).

|0 0 1|

(1/2) |17/11 119/11 1|=Area

|-51 -68 1|

What I have attempted to depict here is a 3x3 determinant multiplied by 1/2; the components in the first 2 columns are the vertices taken in counterclockwise order and the 3rd row is simply all 1's.

The derivation of this formula is too complicated to show here...it involves seeing the picture of the triangle and component triangles that make it up. The only reference I have is out of print, but if you are interested, I will try to send you the derivation.