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

Definite Integrals

What is a definite integral?

• This is known as the Fundamental Theorem of Calculus

• a and b are called limits

  • a is the lower limit

  • b is the upper limit

• is the integrand

• is an antiderivative of

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

  • “+c” would appear alongside both F(a) and F(b)

  • subtracting means the “+c”’s 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

STEP 2

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

STEP 3

Substitute the limits into the function and evaluate