explain the integration method of physics.
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Integration techniques:
1. u-substitution.
2. Reverse chain rule.
3. Partial fraction expansion.
4. Integration using trigonometric identities.
5.Trigonometric substitution.
First you need to pick an axis to integrate to. Do you want to find the area under the curve (x-axis) or next to the curve (y-axis). Next you need to pick you limits. Where does your area go between? 5 and 7? -21 and 2.4? 0 and ∞? Once you have your limits and your axis of choice you can set it all out nice and neat in integral form so it looks something like this
a and b are your limits, how big your area is, which numbers it’s going between. Now say you’ve decided to integrate some horrible equation to find its area. And you’ve decided to work to the x-axis between 0 and 7, like so
What integrating does is basically split it into loads of little bits and add them up e.g. one of the little bits of the graph would be this
Integralgraph2Now the ‘area’ of this bit is just 12. You just assume that it has such a small width that is doesn’t matter and just count the height. So you do this all the way along. The thinner your lines the better your result, so you would also have
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here is your answer mate
Integration generally means addition .It is frequently used in physics for derivation of formula and also it is used for determine area , volume etc of a irregular body.For this first a elementary area or volume is consodered and then integrate it to get the total volume or area.
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