Find the area bounded by $r = a \sin 2\theta$ and $r = a \cos 2\theta$.
What is the area within the curve r2 = 16 cos θ?
Find the area of the inner loop of the limacon r = a(1 + 2 cos θ).
Find the area inside the cardioid r = a(1 + cos θ) but outside the circle r = a.
Find the area individually enclosed by the following Cardioids:
(A) $r = a(1 - \cos \theta)$
(B) $r = a(1 + \cos \theta)$
(C) $r = a(1 - \sin \theta)$
(D) $r = a(1 + \sin \theta)$
Find the area bounded by the lemniscate of Bernoulli r2 = a2 cos 2θ.
Plane Areas in Rectangular Coordinates
There are two methods for finding the area bounded by curves in rectangular coordinates. These are...
- by using a horizontal element (called strip) of area, and
- by using a vertical strip of area.
The strip is in the form of a rectangle with area equal to length × width, with width equal to the differential element. To find the total area enclosed by specified curves, it is necessary to sum up a series of rectangles defined by the strip.