docAP Calculus AB Chapter 6 Worksheet
download 
Plainte Documents pareils
Integral Formulas 1. ∫ u du = 1 n + 1 u + c if n
(c) Write down the 3rd Taylor polynomial P3(x) , for xe−2x , at a = 0 .
MATH 141 Fundamental Theorem of Calculus (FTC) Let f : [a, b] → R
![MATH 141 Fundamental Theorem of Calculus (FTC) Let f : [a, b] → R](http://s1fr.doczz.net/store/data/000158037_1-90738254df74b2352f400181e26e259f-70x70.png "MATH 141 Fundamental Theorem of Calculus (FTC) Let f : [a, b] → R")
If the functions y = f (x) and y = g(x) are differentiable at x and a and b are constants, then:
1. Dx [af (x) + bg(x)] = af 0 (x) + bg 0 (x)
2. Dx [f (x) · g(x)] = f 0 (x) · g(x) + f (x) · g 0 (x)
Recall from Math 141 Integration Basics Fundamental Theorem of
If f is differentiable at x and g is differentiable at f (x), then:
(4) Dx [g(f (x))] = g 0 (f (x)) f 0 (x) .
On this handout, a (∗) means that you do not have to memorize the formula
but should be...
Calculus I Integration: A Very Short Summary Definition
+ C for r 6= −1
r+1
Z
Z
du
= u−1 du = ln |u| + C for r = −1
u
Z
au
au du =
+C
ln a
Z
eu du = eu + C
Z
cos u du = sin u + C
Z
sin u du = − cos u + C
Z
sec2 u du = tan u + C
Z
sec u tan u du = sec u ...
Calculus Tables
If an integrand has the form f (u(x))u (x), then rewrite the entire
integral in terms of u and its differential du = u (x) d x:
