Welcome to Unit 4 - Introduction to Integrals of AP Calculus AB

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Unit 4 - AP Calculus National Objectives

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Students will be able to use techniques of integration to:

Recognize antiderivatives of basic functions.
Interpret the definite integral as the limit of a Riemann sum and express the limit of a Riemann sum in integral notation.
Determine the definite integral of a continuous function f over the interval [a, b], denoted by is the limit of Riemann sums as the widths of the subintervals approach 0. That is, is a value in the ith subinterval, ∆x, is the width of the ith subinterval, n is the number of subintervals, and max ∆x is the width of the largest subinterval. Another form of the definition is is a value in the ith subinterval.
Approximate a definite integral by graphical, numerical, algebraic, and verbal representations.
Calculate a definite integral using areas and properties of definite integrals.
Analyze functions defined by an integral.
Calculate antiderivatives and evaluate definite integrals.
Interpret the meaning of a definite integral within a problem.
Apply definite integrals to problems involving the Average Value Theorem of a function over an interval [a,b] is .
Analyze differential equations to obtain general and specific solutions.
If f is continuous on the interval [a, b] and is an antiderivative of f , then
- The notation .