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# Find the area of the crescent-shaped region (called a $lune$) bounded by arcs of circles with radii $r$ and $R$. (See the figure.)

## $$r \sqrt{R^{2}-r^{2}}+\frac{\pi}{2} r^{2}-R^{2} \arcsin (r / R)$$

#### Topics

Integration Techniques

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CR

Cam R.

September 22, 2020

What is crescent-shaped region?

HC

Howie C.

September 22, 2020

Hey Cam, This problem involves finding the area of a crescent-shaped region also called a lune. This region can be imagined as the region bounded by a larger circle and a smaller circle, such that the larger circle touches the smaller circle internally.

AG

Alex G.

September 22, 2020

Can someone explain what the arcs of circles is?

LP

Lindsey P.

September 22, 2020

Hi Alex, An arc of a circle is a "portion" of the circumference of the circle. The length of an arc is simply the length of its "portion" of the circumference. The circumference itself can be considered a full circle arc length.

ST

Samantha T.

September 22, 2020

Anyone else confused by the Radius , can someone explain?

NH

September 22, 2020

I see how that could be confusing. In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

LE

Leighton E.

January 22, 2021

area of a sector of a circle

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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#### Topics

Integration Techniques

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp