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Integrating Powers of x (CIE AS Maths: Pure 1)
Revision Note
Integrating Powers of x
What is integration?
- Integration is the inverse ('opposite') of differentiation
How do I integrate powers of x?
- For each term …
- … increase the power (of x) by 1
- … divide by the new power
- This does not apply when the original power is -1
- the new power would be 0 and division by 0 is undefined
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Finding the Constant of Integration
How do I find c?
- STEP 1 Rewrite the function into a more easily integrable form
- Each term needs to be a power of x (or a constant)
- STEP 2 Integrate each term and remember “+c”
- Increase power by 1 and divide by new power
- STEP 3 Substitute the coordinates of a given point in to form an equation in c
- Solve the equation to find c
Worked example
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