truthfinder
- 24
- 0
Hi,
We were going over trigonometric integration in Calculus II the other day. I got the basic idea, but get lost when we're doing the u-substitution.
We had a problem like this:
\int cos^3 (x) dx
Then we did:
\int (1 - sin^2 (x)) cos(x) dx
Starting u-substitution:
u = sin(x)
And
du = cos(x) dx
So then we have:
\int (1 - u^2) du
All reasonable so far. But then, du just kind of disappears.
u - u^3/3
Which is
sin(x) - 1/3 sin^3 (x) + c
I see how u-substitution works when its something simple, but I can't see how the answer here can be derived to get what was given before.
We were going over trigonometric integration in Calculus II the other day. I got the basic idea, but get lost when we're doing the u-substitution.
We had a problem like this:
\int cos^3 (x) dx
Then we did:
\int (1 - sin^2 (x)) cos(x) dx
Starting u-substitution:
u = sin(x)
And
du = cos(x) dx
So then we have:
\int (1 - u^2) du
All reasonable so far. But then, du just kind of disappears.
u - u^3/3
Which is
sin(x) - 1/3 sin^3 (x) + c
I see how u-substitution works when its something simple, but I can't see how the answer here can be derived to get what was given before.