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DERIVATIVES AND INTEGRALS
tanh u sech2 uu
dx
d
csch u csch u coth uu
dx
d
u
tanh1 u
dx
1 u2
u
d
csch1 u
dx
u 1 u2
Differentiation Formula
d u
f (t) dt = f (u) " Du
dx ! a
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)
Tabla de Integrales
FORMULAS
Use differentiation and integration tables to supplement differentiation and integration techniques.
Math 220 November 8 I. Evaluate thel indefinite integral. 1. ∫ (e3x +
csc(x)(csc(x) cot(x))dx
u = csc(x)
du = − csc(x) cot(x)dx
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Algebra Geometry - Stewart Calculus
x y3 x 3 3x 2 y 3xy 2 y 3
x y3 x 3 3x 2 y 3xy 2 y 3
x yn x n nx n1y
Recall from Math 141 Integration Basics Fundamental Theorem of
sec u tan u du = sec u + C
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sin u du = − cos u + C
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