Question

Integrals

Answer 1

\[\Large\rm \cos \theta\left[\frac{\sin \theta}{\cos \theta}+\frac{1}{\cos \theta}\right]\]Distribute the cos theta, should simplify things down quite a bit.

Answer 2

so

\[\frac{ \cos(\theta)\sin(\theta) }{ \cos(\theta) }+\frac{ \cos(\theta) }{ \cos(\theta) }\]

Answer 3

The cos's cancel each other leaving sin(theta)+1 ?

Answer 4

Mmm yah looks good!
Understand how to integrate those two terms?

Answer 5

I know how to do it without the trig functions, first time seeing them with integrals

Answer 6

When you take derivatives of your sine function it follows this pattern that I'm sure you're familiar with:\[\Large\rm \sin x\to \cos x\to -\sin x\to -\cos x\]And then it repeats that process. Errr lemme show just a few more on each side,\[\Large\rm -\cos x\to\sin x\to \cos x\to -\sin x\to -\cos x\to \sin x\]

For integrating we just go backwards:\[\Large\rm -\cos x\leftarrow\sin x\leftarrow \cos x\leftarrow -\sin x\leftarrow -\cos x\leftarrow \sin x\]

Answer 7

So for sine, it just brings us back to uhhhh -cosine, yes?

Answer 8

right

Answer 9

so it would be x - cos(x)

Answer 10

Yah good job!
With some type of +C on the end if you want.

Answer 11

right, yeah. Thanks!