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the graph of a piecewise linear function f, for -1<x<4. what is the value of integral (-1 to 4) F(x) dx?

the interval i gave is grerater than or equal to and less than and equal to. i didn't know how to put the underscore under the symbol. for the integral, -1 is on the bottom of the integral symbol and 4 is on the top.

anyway, since i can't draw the graph, here are the points: (-1,0) (0,2) (1,2) (2,0) (3,-1) (4,-1)

the ilnes connecting the dots is straight, no curves and stuff.

if you look at the overall graph, i can separate it into triangles and squares. so i did that and i added up the total area of each shape and got

the second way i did it:
when i drew the graph, part of it is under the x-axis so when i was trying to find the area, i subtracted that from the the area of the other part of the graph and i got 4.

this is a multiple choice question, both the answers were in there, so now i'm confused. which one is right?

sorry if my explanation is to wordy or confusion. did the best i can

If I'm not mistaken, wouldn't the answer be 2.5? I have the exact same problem in front of me; I approximated using rectangles (half values for triangles). The area above the curve was 4, and below was 1.5... shouldn't you subtract the 1.5 from the 4?

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  1. my name ! :)

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