Just started integrals and I already have a question.

[pinkphiloyd]

I thought I was good with derivatives. I'm trying to think about this as working backwards in my brain and I seem to be having some sort of mental hiccup.

I've watched all the Khan academy antiderivative videos a couple of times now. I was working on the practice problems and did pretty well until I got to

"evaluate the integral cos x/sin^2 x"

It's just occurred to me that I don't know how to use notation in a forum to describe where I'm getting confused. This is a problem on a problem. I'm going to attach a picture. I apologize if there's a better way to do this.

You'll see the problem in the attachment. I understand the way the problem was re-written. The problem is, in my brain, the answer provided is the solution to find the integral of (sin x)^-2. What happened to that original cos x?

I felt like a big enough idiot before I attempted to explain this here.

 

[Deleted member 4993]

I thought I was good with derivatives. I'm trying to think about this as working backwards in my brain and I seem to be having some sort of mental hiccup.

I've watched all the Khan academy antiderivative videos a couple of times now. I was working on the practice problems and did pretty well until I got to

"evaluate the integral cos x/sin^2 x"

It's just occurred to me that I don't know how to use notation in a forum to describe where I'm getting confused. This is a problem on a problem. I'm going to attach a picture. I apologize if there's a better way to do this.

You'll see the problem in the attachment. I understand the way the problem was re-written. The problem is, in my brain, the answer provided is the solution to find the integral of (sin x)^-2. What happened to that original cos x?

I felt like a big enough idiot before I attempted to explain this here.

start with substitution:

u = sin(x)

du = cos(x) dx

continue.....

 

[pinkphiloyd]

start with substitution:

u = sin(x)

du = cos(x) dx

continue.....

Thanks for your help. I almost get this. the concept is further illustrated in this second attachment. But for some reason I'm having difficulty wrapping my brain around the first step. Why do you have 1 in the numerator as opposed to -sin x?

 

[pinkphiloyd]

Wait. I just found "U substitution" in one of the texts I use. I think somehow I got myself out of order on the Khan stuff. Thanks again for the help and sorry for the confusion. I'll check back for more insight, though!