Page:Calculus Made Easy.pdf/240

 of all the little triangles making up the required area.

The area of such a small triangle is approximately $$\dfrac{AB}{2}\times r$$ or $$\dfrac{r\, d\theta}{2}\times r$$; hence the portion of the area included between the curve and two positions of r corresponding to the angles $$\theta_1$$ and $$\theta_2$$ is given by

Examples.

(1) Find the area of the sector of $$1$$ radian in a circumference of radius $$a$$ inches.

The polar equation of the circumference is evidently $$r=a$$. 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 $$r=a(1+\cos \theta)$$.