Mathematics (AS)·Integration · NSSCAS 1.9.1
Integration as reverse differentiation
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Integration is differentiation played backwards — and this lesson makes it feel that simple. You will learn the reverse power rule, integrate polynomials, square roots and negative powers, and master the bracket pattern (ax + b) to the power n. Then you will use a point on a curve to pin down the constant of integration and write the exact equation of the curve. By the end, the stretched S symbol will feel like an old friend.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.9.1):
- Interpret integration as the reverse process of differentiation, and integrate (ax + b)ⁿ for any rational n except −1, together with constant multiples, sums and differences
- Solve problems involving the evaluation of a constant of integration, e.g. find the equation of the curve through (1, −2) for which dy/dx = 2x + 1
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