Integration (1 Viewer)
- Thread starter mac1996
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Shadowdude
Cult of Personality
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Integration is just finding the area under the curve, pretty much.
So you just... add or subtract the areas using your Year 7 or 8 techniques.
Add the stuff above the x-axis. Subtract the stuff below the x-axis...
So you just... add or subtract the areas using your Year 7 or 8 techniques.
Add the stuff above the x-axis. Subtract the stuff below the x-axis...
Carrotsticks
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I presume the top limit is 4.
Break up the total area into many little pieces, and find the area of each individual piece.
If the piece is below the x axis, then it is considered 'negative area' and if it is above the x axis, it is considered 'positive area'.
So for example, from 0 to 1 in (a), we have pi/4 because it is a quarter of a circle of radius 1.
However, from 1 to 2 in (a), we have -1/2 because it's a half of a square with side length 1, but it is BELOW the x axis, so it is negative.
Repeat this process for each 'piece' and add them all up (don't worry if you get a negative answer, that is okay).
Break up the total area into many little pieces, and find the area of each individual piece.
If the piece is below the x axis, then it is considered 'negative area' and if it is above the x axis, it is considered 'positive area'.
So for example, from 0 to 1 in (a), we have pi/4 because it is a quarter of a circle of radius 1.
However, from 1 to 2 in (a), we have -1/2 because it's a half of a square with side length 1, but it is BELOW the x axis, so it is negative.
Repeat this process for each 'piece' and add them all up (don't worry if you get a negative answer, that is okay).
