00:01
Here i'm going to work some examples of integrating cosine and sine functions.
00:08
And most of what you wind up doing, except for some special cases, is integrating something like cosine of 3x or sign of 2x.
00:20
And the thing to remember is integrating is the inverse function of differentiating.
00:26
So the integration of a cosine function will give you a sign.
00:30
And the integration of a sign function will give you a minus cosine.
00:36
And by the chain rule, if you took the derivative of sine of ax with respect to x, the a would come out as a chain rule product.
00:50
So if you're integrating, it winds up in the denominator.
00:54
Likewise with integrating sine of bx, the b shows up in the denominator.
01:01
So let's take a look at some examples, and there will be one interesting example.
01:09
But this is actually a vector function, which can be broken up into three separate integrals, one for the x direction.
01:18
So we'll just kind of use the little vector notation to work in separate space.
01:26
So we have cosine of 13t dt.
01:31
Okay, now the 6 is just a constant.
01:37
No surprise there, but the integral of the cosine is sine of 13t over 13 between 0 and pi over 2.
01:50
And there it's a definite integral.
01:54
So we simply take the difference between the function at its end points.
02:00
13 over 2 pi minus sine of 0.
02:08
Of 0 is just 0, and 13 pi is the same thing as 6 plus 1 half pi...