Circumference of a circle Use calculus to find the circumference of a circle with radius a.

Problem 42E

Circumference of a circle Use calculus to find the circumference of a circle with radius a.

Solution

Step 1

In this problem we have to find the circumference of a circle with radius .

The Cartesian equation of a circle of radius a with its center at (0,0) is given by,

where

In the first quadrant,

Differentiating with respect to x on both sides, we get

Squaring on both sides we get