Peter K. answered • 01/25/20
Math / Statistics / Data Analytics
The question is not formatted correctly. I assume that it is asking for the integral from -3 to 5 of f(x)dx. The question or the diagram don't say what f(x) is. I will assume that the blue line is a graph of f(x). The diagram also does not indicate the variables that the axes represent. I will assume that the horizontal axis is x and the vertical axis is y or f.
Our integral consists of the sum of the signed areas under the curve of three parts, the first trapezoid, let's call it's area B, the second area, call it -B, and the red area, call it -A, since its area is given as A, the integral, or the signed area under the curve from 3 to 5 is actually negative A.
So the sum of the signed areas, or the requested integral, is B - B - A, or -A.
An answer, which says, "The total area is 8 + A units" answers a different question. This response would be for the area between the x axis and the curve, f(x). In that case, negative and positive areas would not cancel each other. Such an area is NOT an integral.
