So, I've got to get back into the routine of doing these things. Luckily my dad's got my back and remembered for me.
Calculus. Right. Here I go...
A brief overview of basic integration (a few tips):
1. Remember that normally your u is whatever is being raised to a power or under the square root or the bottom of a fraction, etc. For example:
∫x/√(x^2+1)
u=x^2+1
du=2x
Now balance the 2 by putting a ½ in front and you have:
1/2∫du/(√u)
=√(x+1) + C
2. You have to be able to recognize basic derivatives (i.e. trig ones) So:
∫secx tanx
We know that the derivative of sec x is sec tan, so obviously the integral equals:
secx+C
3. Also remember that if you see 1/x and your integrating..that’s natural log integration.
4. Okay. By parts. You must remember that the formula is as follows:
uv- ∫(v)du
That, my friends is a crucial part. Also remember that your u is usually that which will decrease more. So if you have x and x^3, your u would be x and dv x^3. Got it? Good. HOWEVER, if you have a ln in the equation, that needs to be your u because you cannot integrate a ln…It’s just not conducive.
5. Next subject: Trig Substitution. I know we had some homework over the weekend, and for a lot of it, I was unsure. I did find out, I believe, that the integral of sec x is always going to be:
∫secx = ln(secx + tanx) + C
Don’t ask me why, that’s just what I found. You have to memorize it I believe? Now my main problem is trying to figure out when to substitute in certain trig identities. Does anyone know a way to remember it ? In desperate need of help if I’m going to pass that quiz on Wednesday. Muchas Gracias!
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ReplyDeleteMal
ReplyDeleteThe way I usually figure out what to substitute for my trig. terms is what going to be easiest, but that's easier said than done.
I usually try to get all my trig terms into the same thing, like sine, or at least relating to one another, like sine and cosine, otherwise if you have something unrealating, like cosecant and tangent, then you will often run into problems.
Ryan
what i do malerie, is pretty much anytime i see something raised to a degree higher than 2, i start pulling out a squared, and then changing that.
ReplyDeletelike if i had S tan^3x
i automatically would do this
tanx tan^2x
then after that.. i always convert my tan^2x to sec^2x - 1
and just work it from there. it's become sort of automatic for me to do that