Hi I had an explanation to this question before but don't get where the numbers came from, as in why each number was so, here's the link , its problem #9 : http://www.baruch.cuny.edu/sacc/documents/2205AdditionalProblemsfortheFEM.pdf
The answer broke down each section :
-1 to 0 has area : (1/2) (1 x 2) = 1
0 to 1 has area : (1 x 2) = 2
1 to 2 has area (1/2) x (1 x 2) = 1
2 to 3 has area : (1/2) (1x1) = -1/2
3 to 4 has area : (1 x 1 ) = -1
I don't get where 1/2 comes from and where all the rest of the numbers in the calculations come from.
The answer broke down each section :
-1 to 0 has area : (1/2) (1 x 2) = 1
0 to 1 has area : (1 x 2) = 2
1 to 2 has area (1/2) x (1 x 2) = 1
2 to 3 has area : (1/2) (1x1) = -1/2
3 to 4 has area : (1 x 1 ) = -1
I don't get where 1/2 comes from and where all the rest of the numbers in the calculations come from.
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The interval of integration, [-1,4], has to be split everywhere the function changes. This particular function changes every interval of length 1. From -1 to 0 it's a triangle length 1 and height 2. So that area is (1/2)(1 * 2), one-half the base times the height. From 0 to 1 it's a rectangle of height 2 and length 1. The rest of the intervals are similar. From 2 to 3 and 3 to 4 the function is below the x-axis, so the area is taken to be negative. If you add up all these you'll get the total area.
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wait from 2 to 3 what shape is that I know length is 1, and same from 3 to 4?
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http://www.analyzemath.com/Graphing/piecewise_functions.html