Question

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

Answer 1

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

Answer 2

Did you graph the lines?
Let the points a,b,c,d be on the x-axis 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 x-axis, 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

Answer 3

no, the answer is 6, you separate the triangles, find the area and add them up