Chapter 7: Additional Applications of Integration
Section 7.2: Integration in Polar Coordinates
Example 7.2.9
Starting with the expression for the arc length of a curve defined parametrically, obtain the expression for the arc length of a curve defined by in polar coordinates. (See Table 7.2.1.)
Solution
Mathematical Solution
From Table 5.4.1, the arc length of the curve defined parametrically by the equations is given by the integral
The equations convert the polar curve to Cartesian coordinates with now the parameter. Hence, the radicand in the integrand becomes
from which it follows that
as per Table 7.2.1.
Maple Solution
Define the parametric equations and
Context Panel: Assign Function
Obtain the radicand of the integrand for the arc-length integral
Write the sum of the squares of the derivatives. Press the Enter key.
Context Panel: Simplify≻Simplify
The expression for in Table 7.2.1 is now easily obtained.
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