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Year 12 · Calculus

Integrate polynomials

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

Find ∫ (4x³ + 3) dx
Reverse the power rule: raise the power by one and divide by the new power. ∫4x^3 dx = 4/4 x^4 = 1x^4, ∫3 dx = 3x. Don't forget + c.
Answer: x^4+3x+c

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Do not forget + c.

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