AP Calculus AB 8.5 Finding the Area Between Curves Expressed As Functions of Y Questions

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.

$\int_{0}^{k}\left(5-y-e^{y}\right) d y=\frac{1}{2} \cdot 2.986\left(\right.$ or $\left.\frac{1}{2} \cdot 2.985\right)$

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Covered syllabus points

Question 1