Definite Integrals (DP IB Applications & Interpretation (AI)): Revision Note

Definite Integrals

What is a definite integral?

• A definite integral is written in the form , where

  •  is the integrand (function to be integrated)

  • and are the integration limits

    • is the lower limit, and is the upper limit

    • These correspond to the lines and in the area under a curve

• According to the Fundamental Theorem of Calculus, if  is an antiderivative of, then

• The constant of integration (“”) is not needed in definite integration

  • "” would appear alongside both F(a) and F(b)

  • Then subtracting means the “”’s would cancel

How do I find definite integrals analytically (manually)?

• STEP 1

  Give the integral a name to save having to rewrite the whole integral every time

  If need be, rewrite the integral into an integrable form

  • E.g.

• STEP 2

  Integrate without applying the limits; you will not need “+c”
  Notation: use square brackets [ ] with limits placed at the end bracket

  • E.g. 

•  STEP 3

  Substitute the limits into the function and evaluate

  • E.g.