You have three line segments and you are given four points. You have to find the Integral. The full question is in the description.

Question

You are given the four points in the plane a=(-2,1), b=(3,-6), c=(7,4), and d=(10,-2). The graph of the function consists of the three line segments AB, BC and CD. Find the integral by interpreting the integral in terms of sums and/or differences of areas of elementary figures.  Find the integral from -2 to 10 f(x) dx

Answer 1

It is necessary to find the x values when f(x)=0, the x-axis crossings. I found them to be

-3/5, 54/10, and 9 (I used find slope and use equation m=(y-y₀)/(x-x₀) and set y=0)

check my work.

Then draw triangles, four, where the base is known on the x-axis and height is y value vertex

height is negative for two triangles.

area=1/2*base*height four each and the two triangles below x-axis are negative area.

I calculate -111/10 as summed area.

check my work.