Calculus II Formula Sheet
Area Formulas
• Area of a square: A = s
• Area of a circle/disc: A = πr2
2
• Area of a semicircle: A = 12 πr2
• Surface area of a cylinder/shell: SA = 2πrh
Trigonometric Identities
2
2
• 1 − cos (θ) = sin (θ)
• sin2 (θ) = 21 (1 − cos (2θ))
• 1 − sin2 (θ) = cos2 (θ)
• cos2 (θ) = 12 (1 + cos (2θ))
• tan2 (θ) + 1 = sec2 (θ)
• sin (2θ) = 2 sin (θ) cos (θ)
• sec2 (θ) − 1 = tan2 (θ)
c
• For a right triangle:
b
a
Integral Formulas
Z
xn+1
•
xn dx =
n+1
Z
•
ex dx = ex + C
Z
•
sin x dx = − cos x + C
Z
•
cos x dx = sin x + C
Z
•
sin θ = cb , cos θ = ac , tan θ = ab , sec θ = ac
Z
2
sec x dx = tan x + C
•
1
dx = ln |x| + C
x
Z
•
sec x tan x dx = sec x + C
Z
• Integration by parts:
Z
•
sec x dx = ln | sec x + tan x| + C
Z
•
Z
•
Z
u dv = uv −
x
1
1
dx
=
arctan
+C
x 2 + a2
a
a
sec3 x dx = 12 sec x tan x + 12 ln | sec x + tan x| + C
• The p-series
∞
X
1
n=1
n
p
Series
converges for p > 1 and diverges for p ≤ 1.
• The geometric series
∞
X
n=a
rn converges to
ra
for |r| < 1 and diverges for |r| ≥ 1.
1−r
Special Limits
x
x
1
x+1
• lim x1/x = 1
• lim 1 +
= lim
=e
x→∞
x→∞
x→∞
x
x
sin x
x
• lim
=1
x
1
x→0 x
• lim
=
x→∞
x+1
e
v du