1. Definite Integrals
Rizzi – Calc BC

2. Limits of Riemann Sums
As we take more and more subintervals, we get closer to the actual approximation of the area under the curve.

3. Limits of Riemann Sums Cont.

4. 𝑨𝒓𝒆𝒂= 𝒂 𝒃 𝒇 𝒙 𝒅𝒙 Definite Integrals
If f is continuous, then the area under the curve on [a, b] is represented by:
𝑨𝒓𝒆𝒂= 𝒂 𝒃 𝒇 𝒙 𝒅𝒙

5. Areas of Common Geometric Figures

6. Properties of Definite Integrals
Draw a picture representing each of these properties

7. Properties of Definite Integrals Cont.
Draw a picture representing this property:

8. Properties of Definite Integrals
Draw a picture representing each of these properties

9. 2 6 24 Example Problem Given 𝟎 𝟒 𝒇 𝒙 𝒅𝒙=𝟖 and 𝟒 𝟕 𝒇 𝒙 𝒅𝒙=−𝟐 Find:
c) 𝟕 𝟒 𝒇 𝒙 𝒅𝒙 =
b) 𝟎 𝟕 𝒇 𝒙 𝒅𝒙 =
d) 𝟎 𝟒 𝟑𝒇 𝒙 𝒅𝒙 = 2 6 24