Exam 1 Formulas Flashcards
1
Q
integration by parts
A
∫u dv = uv - ∫v du
2
Q
d/dx arcsin
A
1/√(1-x²)
3
Q
d/dx arccos
A
-(1/√(1-x²))
4
Q
d/dx arctan
A
1/(1+x²)
5
Q
√(a²-x²)
A
x=asinθ
6
Q
√(a²+x²)
A
x=atanθ
7
Q
√(x²-a²)
A
x=asecθ
8
Q
trapezoidal rule
A
Δx/2( f(x0) + 2f(x1) + … + 2f(x(n-1)) + f(xn)
9
Q
p-series convergent integrals
A
∫1/(x^p)dx (p>1)
10
Q
p-series divergent integrals
A
∫(1/x^p) (p=<1)
11
Q
∫tanx dx
A
ln|secx| + C
12
Q
∫cotx dx
A
ln|sinx| + C
13
Q
∫secx dx
A
ln|secx + tanx| + C
14
Q
∫cscx dx
A
ln|cscx - cotx| + C
15
Q
∫sin²x dx
A
x/2 - sin2x/4 + C
16
Q
∫cos²x dx
A
x/2 + sin2x/4 + C
17
Q
volume by slicing formula
A
∫A(x) dx (evaluated from a to b)
18
Q
disc/washer method
A
V = ∫πr² dx (evaluated from a to b)
19
Q
∫csc(x)cot(x) dx
A
-csc(x) + C
20
Q
∫sec(x)tan(x) dx
A
sec(x) + C
21
Q
∫csc²(x) dx
A
-cot(x) + C
22
Q
∫sec²(x) dx
A
tan(x) + C
