7.2 Calculus of Parametric Curves

[STARTS AT 14:53]

Instructor: So we're going to take these two functions and find the arc length of this semicircle. So our length equals the integral from 0 to pi of the square root of x prime squared. Well x prime is going to be 3, negative 3. Let's write that again. Negative 3 sine t. And the derivative of this is 3 cosine t. And we're going to square both of those. OK. 

Well squaring that, we get 9. 0 sine squared t plus 9 cosine squared t. Hopefully you notice we can factor the nine out. So this is actually three. I could factor it out of the integral as well. 3 square root of sine squared t plus cosine squared t. Now the Pythagorean identity tells me that is actually equal to 1. So when I take the antiderivative of-- so this is times 1 here. The antiderivative of that is 3t evaluated from 0 to pi, Which will be 3 pi. 

[ENDS AT 16:33]