of all the little triangles making up the required area.
The area of such a small triangle is approximately or ; hence the portion of the area included between the curve and two positions of r corresponding to the angles and is given by
.
Examples.
(1) Find the area of the sector of radian in a circumference of radius inches.
The polar equation of the circumference is evidently . The area is
.
(2) Find the area of the first quadrant of the curve (known as “Pascal’s Snail”), the polar equation of which is .