Q. 28 - Calculus

Question

The arc length of polar functions: Find the arc lengths of the following polar functions.   

$r=a \sin \theta +b \cos \theta , \mathrm{where} a \mathrm{and} b \mathrm{are} \mathrm{positive} \mathrm{constants} \mathrm{for} \theta \in [0, \pi ]$

Step-by-Step Solution

Answer

The arc length is $2\sqrt{\left(a^2+b^2\right)}\mathrm{\pi } \mathrm{units}$

Step 1: Given information.

The curve is $r=a \sin \theta +b \cos \theta , \mathrm{where} a \mathrm{and} b \mathrm{are} \mathrm{positive} \mathrm{constants} \mathrm{for} \theta \in [0, \pi ]$

Step 2: Arc length.

The length of an arc is given by,