Definite Integrals Rizzi – Calc BC.

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Presentation transcript:

Definite Integrals Rizzi – Calc BC

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

Limits of Riemann Sums Cont.

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

Areas of Common Geometric Figures

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

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

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

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