Clarence
  • Clarence
How would I determine an integral function using a graph?
Mathematics
katieb
  • katieb
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Clarence
  • Clarence
This question in particular:
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FireKat97
  • FireKat97
the definite integral of a function between two numbers, is the area under the graph of the function between the two numbers. Ie, in your question, the definite integral you need to find is the area of the graph under f(x) between the points x= 0 and x = 28. Because your graph is essentially composed of straight lines, you can manually find the area by breaking it up into rectangles and triangles and sum the two areas together. Note, the larger (area 1) is a positive "area" (above the x axis) whereas the smaller area (area 2) is a "negative" area (under the x-axis) so when you go to "sum" them together do area 1 + (- area 2)
FireKat97
  • FireKat97
Hope that makes sense :)

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Clarence
  • Clarence
Oh, I think I get it! So just quickly looking at the graph, would the answer just be 18 then? :P @FireKat97
FireKat97
  • FireKat97
Actually @Clarence I meant something like this...
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Clarence
  • Clarence
Oh right, so it'd be 32 then :p
Clarence
  • Clarence
So for area 1, it'd be 7x3+1/2(12x3) and area 2 as 5+2 right? @FireKat97
FireKat97
  • FireKat97
Yup, thats the basic idea. but using fractions will add accuracy :)

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