Page:Calculus Made Easy.pdf/234

 N.B–Notice that in dealing with definite integrals the constant $$C$$ always disappears by subtraction.

Let it be noted that this process of subtracting one part from a larger to find the difference is really a common practice. How do you find the area of a



plane ring (Fig. 56), the outer radius of which is $$r_2$$ and the inner radius is $$r_1$$? You know from mensuration that the area of the outer circle is $$\pi r_2^2$$; then you find the area of the inner circle, $$\pi r_1^2$$; then you subtract the latter from the former, and find area of ring $$= \pi(r_2^2 - r_1^2)$$; which may be written

= mean circumference of ring × width of ring.