We want to focus on the definite integral of a polynomial function. These arise very commonly in calculus, so here are detailed solutions to two problems, one multiple-choice and one free-response, involving a definite integral of polynomial.   Free-Response Definite Integrals: You will not commonly be asked to evaluate common definite integrals on the free-response, […]

The free response portion of an AP Exam (also officially known as Section II) is very important, and the AP Calculus AB free response is no different. In fact, the AB free response section is weighed equally with your multiple choice results. It also turns out that the structure of the AB and BC Exams […]

Did you know that a graph of a function f is not the same as the function itself? It might seem like there is clearly a difference, but sometimes it’s hard to articulate into words. We have spoken about the definition of a function. Simply put, it’s a rule that transforms one real number into […]

Warm-up: Keeping with the theme of volume of solids of revolution, try this multiple choice question, which should need only understanding of the geometric meaning of the definite integral as a measurement of volume. Question: A solid is generated by revolving the region enclosed by the function , and the lines x =2, x =3, y […]