Integration Revision 2

Oliver Seglah 12J

Integration – The basics Integration is the reverse of differentiation. It can be used to calculate the area between the curve of a function and the axis. If we are given ∫

then we do With respect to x

Example: 3𝑥 2 − 6𝑥 3𝑥 2 1 2 1

−

4 𝑑𝑥

6𝑥 1 1

4𝑥 0 1

1 1

0 1

3𝑥 3 6𝑥 2 − 3 2 𝑥 3 − 3𝑥 2

4𝑥 1 4𝑥

There is always a constant at the end unless we are given limits!

𝑐

𝑐 𝑐

Fractions If we are given something like ∫

4 2

don’t worry!

Just use indices rules to get it in the format ∫

.

Use indices rules for roots as well! Example: 4 𝑑𝑥 ≡ 𝑥2 4𝑥 −2 1

−1

−4𝑥 −1

4𝑥 −2 𝑑𝑥

𝑐

−2 1 4𝑥 −1

4 1 × 𝑑𝑥 ≡ 1 𝑥2

𝑐 𝑐 or −

𝟒 𝒙

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