Posted by Anonymous on .
You are given the four points in the plane A = (3,7), B = (1,6), C = (4,6), and D = (6,1). The graph of the function f(x) consists of the three line segments AB, BC and CD. Find the integral interval 3 to 6 f(x)dx by interpreting the integral in terms of sums and/or differences of areas of elementary figures.
I got 18.4555, but it was wrong

calculus 
Anonymous,
i tried a different approach and got 1.5 but its still wrong

calculus 
Steve,
Did you graph the lines?
Let the points a,b,c,d be on the xaxis above or below A,B,C,D
AabB is a trapezoid with bases 7,6, height 2
BbcC is a rectangls 5x6
CcDd is a triangle of height 7 and width 2
However, part of the triangle is below the xaxis, making it a negative area.
Positive area is a triangle 6 by 12/7
Negative area is a trapezoid with bases 12/7 and 2, height 1
Add the areas:
[(7+6)/2 * 2] + [5*6] + [6 * 12/7 * 1/2]  [(12/7 + 2)/2*1]
= 13 + 30 + 36/7  13/7
= 43  23/7 = 39 5/7 = 39.71
better check my math here 
calculus 
Anonymous,
no, the answer is 6, you separate the triangles, find the area and add them up