This week in Calculus BC was pretty good.
Tuesday we re-learned Integration by-parts.
Integration by-parts:
Sudv = uv - Svdu
Example:
Sxe^(x)dx
Pick a u and dv and derive/integrate:
u = x du = 1 dx
dv = e^x(dx) v = e^x
You then plug these into your equation:
xe^(x) - Se^(x)dx
And solve:
xe^(x) - e^(x) + C
We also reviewed "Chasing the Rabbit"
This method of integration happens when you have an e term and a trig term in an integration problem and you basically keep integrating by-parts until you arrive at an integration term the same as you started off with, you them set everything you have equal to the original problem.
We learned something brand new this week that I'm having a little trouble with: Trig Integration.
I get the basic problems, but I was having issues with the homework over the weekend.
Two examples would be:
Ssec^3(pix)dx
and
Stan^5(x/2)dx
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Can anyone help with Ryan's Ssec^3(pix)dx?
ReplyDeleteCause I need help too with that!
Would you pull out a sec^2(pix)?
(sec^2(pix))sec(pix)
=(1+tan^2(pix))sec(pix)
sec(pix) + sec(pix)(tan^2(pix))
I have no idea if this is right, but this is what I would attempt...then I have no clue!
yes abbey you are right... then after that you would separate sec(pix) + sec(pix)tan^2(pix) into two integrals. then integrate with formula for sec(pix) and substitution for sec(pix)tan^2(pix)
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