AP Calculus AB Cha 5 A Calculate Areas in the Plane Using the Definite Integral Topic 8 5 Questions

Practise area-between-curves questions by identifying intersections, choosing top-minus-bottom and evaluating a definite integral.

Exam points

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

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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AP Calculus AB Cha 5 A Calculate Areas in the Plane Using the Definite Integral Topic 8 5 Questions question 1