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##### What is the use of integration...?

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Integration is used to find areas, volumes, central points and many useful things. But it is mostly used to find the area under the curve. In detail integration is very useful to solve in engineering and science problems as follows.
1. For find area under a curve.
2. For find area in between the two curves.
3. We have already learnt in our primary school that areas of shapes (e.g. area of a square, rectangle, triangle etc). But for finding areas when the sides are curved we use integration.
4. To find the volume of an object with curved sides, e.g. wine barrels.
5. To find the centroid of an area with curved sides we use integration.
6. Integration also use when the shape has curved sides. For example moments of Inertia explain how to find the resistance of a rotating body
7. Because the integrated area is being rotated around the axis under the curve so we can use disk integration to find the volume.
8. Electric Charges have a force between them that varies depending on the amount of charge and the distance between the charges. We use integration to calculate the work done when charges are separated.
9. For find the average value of a curve can be calculated using integration.
10. Applications of the Indefinite Integral shows how to find displacement (from velocity) and velocity (from acceleration) using the indefinite integral. There are also some electronics applications.

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##### SHORTCUT TRICKS (Division)
• Divisible by 2 Shortcut trick
• Divisible by 3 Shortcut trick
• Divisible by 4 Shortcut trick
• Divisible by 5 Shortcut trick
• Divisible by 6 Shortcut trick
• Divisible by 7 Shortcut trick
• Divisible by 8 Shortcut trick
• Divisible by 9 Shortcut trick
• Divisible by 10 Shortcut trick