Final Formulas Flashcards
1
Q
Arc length of a curve
A
int sqrt(1 + f’(x)^2)
2
Q
Arc length of a parametric curve
A
int sqrt(dx^2 + dy^2)
3
Q
Arc length of a cartisian graph
A
int sqrt(r^2 + dr^2)
4
Q
Surface area of a curve
A
2π int r(x) sqrt(1 + f’(x)^2)dx
where r(x) gives you your radius
5
Q
Area underneath a parametric curve
A
int y(t)x’(t)dt
6
Q
C - x^2 trig sub
A
sin(x)
7
Q
C + x^2 trig sub
A
tan(x)
8
Q
x^2 - C trig sub
A
sec(x)
9
Q
sin^2(x) half angle identity
A
1/2 - cos(2x)/2
10
Q
cos^2(x) half angle identity
A
1/2 + cos(2x)/2
11
Q
sin^2(x) integral
A
1/2 x - 1/4 sin(2x)
12
Q
cos^2(x) integral
A
1/2 x + 1/4 sin(2x)
13
Q
arctan(x) derivative
A
1 / (1 + x^2)
14
Q
arcsin(x) derivative
A
1 / sqrt(1 - x^2)
15
Q
arccos(x) derivative
A
-1 / sqrt(1 - x^2)
