AP Calculus AB Pacing and Alignment Guide

Chapter 5 Solutions Manual (Access Restricted)

5.1 Learning Targets

I understand how the area under a curve can be expressed as the limit of a sum of areas of thin rectangles (including functional height of right hand, left hand, and midpoint values).

I can use sigma notation to represent a Riemann Sum.

I can approximate the area under curves using rectangles (foreshadowing the right hand, left hand, and midpoint sums covered in 5.2).

5.2 Learning Targets

I understand the definite integral can be interpreted as the area under a curve if the function is above the x-axis and the net area if the function goes below the x-axis.

I can approximate a definite integral by using a left Riemann Sum, Right Riemann Sum or Midpoint Sum.

I can use the properties of the definite integral to evaluate definite integrals. I can evaluate an integral by interpreting it in terms of area (geometric shapes).

5.3 Learning Targets

I understand the precise interpretations of both parts of the Fundamental Theorem of Calculus (FTC1 and FTC2).

I can use the Fundamental Theorem of Calculus Part I (FTC1) to find the derivative of a function.

I can evaluate a definite integral using the Fundamental Theorem of Calculus (FTC2).

5.4 Learning Targets

I can find the most general antiderivative of a function (emphasis on the relationship between a function and its antiderivative stated by the FTC).

I can find the most general antiderivative of a real world problem (both functional models and numerical table interpretations).

5.5 Learning Targets

I can evaluate an indefinite integral using the substitution rule.

I can evaluate a definite integral using the substitution rule.