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Year 12 · Calculus

Definite integrals

Integration undoes differentiation: raise the power by 1 and divide by the new power.

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How to do it

  1. For each term: xⁿ becomes xⁿ⁺¹ ÷ (n + 1).
  2. Add + c for an indefinite integral.
  3. Definite integral: substitute the top limit minus the bottom limit.

Worked example

Evaluate ∫ from 2 to 4 of (12x³ − 5) dx
Antiderivative: F(x) = 3x^4 − 5x. Then F(4) − F(2) = 748 − 38 = 710.
Answer: 710

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Do not forget + c.

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