Calc II Flashcards
integrate:
xn dx
xn+1
n+1
integrate:
k dx
kx + C
integrate:
ex dx
ex + C
integrate:
ax dx
ax +C
ln|a|
integrate:
1
x
ln|x|+C
integrate:
sin(x) dx
-cos(x) + C
integrate:
cos(x) dx
sin(x) + C
integrate:
sec2(x) dx
tan(x) + C
integrate:
csc2(x) dx
-cot(x) + C
integrate:
sec(x)tan(x) dx
sec(x) + C
integrate:
csc(x)cot(x) dx
-csc(x) + C
integrate:
______1______
√ ￣1-x2￣
sin-1(x) + C
integrate:
1
x2-1
tan-1(x) + C
integrate:
tan(x) dx
ln|sec(x)| + C
integrate:
sec(x) dx
ln|sec(x) + tan(x)| + C
integrate:
1
x2+a2
(1/a) tan-1(x/a)) +C
trig identities:
sin2(x)+cos2(x)
= 1
trig identities:
tan2(x) + 1
sec2(x)
trig identities:
1 + cot2(x)
csc2(x)
trig identities:
cos2(x)
(1/2)(1 + cos(2x))
trig identities:
sin2(x)
(1/2)(1 - cos(2x))
trig identities:
sin(2x)
2 sin(x)cos(x)
trig identities:
cos(2x)
cos2(x) - sin2(x)
substitute:
______
√ a2 - x2
x = a sin(θ)
substitute:
______
√ x2 - a2
x = a sec(θ)
substitute:
______
√ x2 + a2
x = a tan(θ)
formula:
Area under a Polar Curve
∫ 1/2 πr2
formula:
Integration By Parts (∫ udv)
∫udv = uv - ∫vdu
formula:
washer method .
pi ∫R^2 - r^2 .
shell method .
2pi ∫ rh dx .
series tests:
if lim an =/= 0 .
an = divergent
nth term test
if lim an = 0 .
INCONCLUSIVE .
if ∫an = definite ..
series is convergent
integral test
uh
if ∫an = indefinite ..
series is divergent
integral test
sum 1
np
p <= 1
divergent
p-series .
∑ 1
np
p > 1
convergent
p-series.
sum of a geometric series
first term
( 1 - ratio)
