AP Calculus BC 8.5 Area with Integrals Overview

Represent the area of a bounded region with definite integrals using vertical or horizontal slices and appropriate bounds.

Exam points

identify the governing calculus relationship in the problem
justify the result with symbolic, graphical or contextual evidence

Covered syllabus points

CHA-5.A—Calculate areas in the plane using the definite integral—Topic 8.5

[Maximum number: 1]

Let R be the region bounded by the graph of $y=\ln x$ , the vertical line $x=e^{2}$ , and the x-axis, as shown in the figure. Which of the following integrals are equal to the area of R ?

I. $\int_{1}^{e^{2}} \ln x d x$
II. $\int_{0}^{2} e^{y} d y$
III. $\int_{0}^{2}\left(e^{2}-e^{y}\right) d y$

I only

III only

I and II only

I and III only

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Covered syllabus points

8.5 Finding the Area Between Curves Expressed as Functions of y question 1