AP Calculus AB 8.5 Area Between Curves Review

Review AP Calculus AB 8.5 by finding intersections, choosing the correct upper-minus-lower setup, and using a definite integral for the enclosed area.

Exam points

find intersection points that set the bounds of integration
integrate top minus bottom to calculate the enclosed area

Covered syllabus points

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

Let R be the region in the first quadrant bounded by the x-axis and the graphs of $y=\ln x$ and y=5-x, as

shown in the figure above.

The horizontal line y=k divides R into two regions of equal area. Write, but do not solve, an equation

involving one or more integrals whose solution gives the value of k.

CALCULUS AB

SECTION II, Part B

Time-60 minutes

Number of problems-4

No calculator is allowed for these problems.

DO NOT BREAK THE SEALS UNTIL YOU ARE TOLD TO DO SO.

$\int_{0}^{k}\left(5-y-e^{y}\right) d y=\frac{1}{2} \cdot 2.986\left(\right.$ or $\left.\frac{1}{2} \cdot 2.985\right)$ $3:\left\{\begin{array}{l}1: \text { integrand } \\ 1: \text { limits } \\ 1: \text { answer }\end{array}\right.$ $3:\left\{\begin{array}{l}2: \text { integrands } \\ 1: \text { expression for total volume }\end{array}\right.$

3: $\left\{\begin{array}{l}1 \text {: integrand } \\ 1 \text {: limits } \\ 1 \text {: equation }\end{array}\right.$

AP ${ }^{\text {® }}$ CALCULUS AB

2012 SCORING GUIDELINES

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Covered syllabus points

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