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AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Monday, January 23, 2006

The method of substitution

We did the integration using the chain rule yesterday. Today, we had some questions on the board. Firstly, we used chain role solved first 3 questions. But if only use chain role, we wouldn't able to solve some problems like 4 and 5, so some new stuff for today. That's the method of substitution.
Three steps: Substitution, antidifferential, resubstitute
Exp:S cos (3x) 3 dx
Let u = 3x
du = 3dx
S cos (u)du= sin u+ C
=sin 3x + C
Another one:
S X/(rt (x +7) dx )
Let u = rt (x+7)
du = 1/2 (x+7) ^-1/2 dx
du = 1/ (2 rt (x+7)) dx
2du = 1/( rt (x+7) ) dx

u= rt (x+7)
u^2 = x +7
u^2-7 = x

S(u^2-7)* 2 du = 2 S( u^2-7) du = 2 ((u^3/3 – 7u))
=(2/3 u^3 -14u+c)
=2/3 (rt (x+7))^3 -14 rt (x+9) + C

Next scribe: Ara

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