Section 4.3 Day 2 Riemann Sums & Definite Integrals AP Calculus BC.

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Presentation transcript:

Section 4.3 Day 2 Riemann Sums & Definite Integrals AP Calculus BC

Learning Targets  Define Riemann Sums  Conceptually connect approximation and limits  Evaluate left hand, right hand and midpoint Riemann Sums of equal and unequal lengths from graphs & tables  Evaluate approximations using the trapezoidal rule  Define a definite integral  Evaluate a definite integral geometrically and with a calculator  Define an integral in terms of area  Apply properties of a definite integral  Define Riemann Sums  Conceptually connect approximation and limits  Evaluate left hand, right hand and midpoint Riemann Sums of equal and unequal lengths from graphs & tables  Evaluate approximations using the trapezoidal rule  Define a definite integral  Evaluate a definite integral geometrically and with a calculator  Define an integral in terms of area  Apply properties of a definite integral

Developing the Riemann Sum and Limit Definition of a Definite Integral Q:How do we get a better approximation of area? So, shrinking the length of the bases for every subinterval so they approach zero leads us to… …Which is the limit definition of the definite integral for f on [a, b]. or the length of each subinterval. Which leads us to…

Definite Integral Definition

Definite Integral Connection to Riemann Sum

Evaluating a Definite Integral As a Limit

Definite Integral Interpretation

Calculator Functions Derivative at a Point: -Click Math, then scroll down to “nderiv” nderiv(expression, variable, value) Integration: -Click Math, then scroll down to “fnint” fnint (expression, variable of integration, lower bound, upper bound) Derivative at a Point: -Click Math, then scroll down to “nderiv” nderiv(expression, variable, value) Integration: -Click Math, then scroll down to “fnint” fnint (expression, variable of integration, lower bound, upper bound)

Calculator Functions

Definite Integral Interpretation

Definite Integral Properties