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Calculus II Formulas
Formulas
31
Mathematics
Undergraduate 1
12/07/2008
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Term
cos(2x)
 Definition
cos^2(x)-sin^2(x)
Term
cos^2(x)
 Definition
1+cos(2x)/2
Term
sin(2x)
 Definition
2sin(x)cos(x)
Term
sin^2(x)
 Definition
1-cos(2x)/2
Term
a^2-u^2
 Definition
u=asin0
Term
a^2+u^2
 Definition
u=atan0
Term
u^2-a^2
 Definition
u=asec0
Term
S du/u
 Definition
ln u +C
Term
S e^u du
 Definition
e^u + C
Term
S a^u du
 Definition
a^u/ln a + C
Term
S cos(u)du
 Definition
sin(u) + C
Term
S sec^2(u) du
 Definition
tan(u)+C
Term
S sec(u)tan(u) du
 Definition
sec(u) + C
Term
S sin(u)du
 Definition
-cos(u) + C
Term
S csc^2(u)du
 Definition
-cot(u) + C
Term
S csc(u)cot(u)du
 Definition
-csc(u)+C
Term
S tan(u)du
 Definition
-ln|cos(u)|+C
Term
S cot(u)du
 Definition
ln|sin(u)|+C
Term
S sec(u)du
 Definition
ln|sec(u)+tan(u)|+C
Term
S csc(u)du
 Definition
-ln|csc(u)+cot(u)|+C
Term
S 1/sqrt(a^2-u^2)du
 Definition
sin^-1(u/a)+C
Term
S 1/a^2+u^2 du
 Definition
1/a tan^-1(u/a)+C
Term
S 1/u*sqrt(u^2-a^2)du
 Definition
1/a sec^-1(|u|/a)+C
Term
Area under the curve =
 Definition
[f(x)-g(x)]dx
Term
Disk method (parallel partition)
 Definition
pi(radius)^2(height)
Term
Washer method (parallel partition)
 Definition
pi[(big radius)^2-(small radius)^2](h)
Term
Shell method (perpendicular partition)
 Definition
2pi(avg. rad)(height)(thickness)
Term
Arc length L
 Definition
sqrt(1+[f'(x)]^2)dx


sqrt(1+[g'(x)]^2)dy
Term
Parametrized arc length
 Definition
sqrt[(dx/dt)^2+(dy/dt)^2] dt
Term
Average Value
 Definition
1/b-a S f(x)dx
Term
Work =
 Definition
S F(x)dx
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