Compiled by: Humber College Math Department
Last revision: 06/2015
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CALC 203
FINAL EXAM FORMULA SHEET
Assume u & v are functions of x.
[ ] [ ] [ ]
2
sec sec tan csc csc cot
d d d d u u v uv
u u u u u u u u uv u v uv
dx dx dx dx v v
′′
−
′ ′ ′′
= ⋅ =−⋅ =+ =
1
1
( 1) ln
1
n
n uu
u
u du C n du u C e du e C
nu
+
= + ≠− = + = +
+
∫∫ ∫
sin cos cos sin tan ln cos u du u C u du u C u du u C=−+ =+ =− +
∫∫ ∫
[ ]
∫∫ −
=
−
=
b
a
b
a
avg dxxf
ab
rmsdxxf
ab
y2
)(
1
)(
1
∫ ∫
−= duvuvdvuPartsBy
θ
[ ] [ ] [ ]
22
sin cos cos sin tan sec [cot ] csc
dd d d
u uu u uu u uu u uu
dx dx dx dx
′′′ ′
= ⋅ =−⋅ = ⋅ =− ⋅
2 22
cot ln sin sec ln sec tan csc ln csc cot
sin2 sin 2
sin cos tan tan
24 24
u du u C u du u u C u du u u C
uu uu
u du C u du C u du u u C
= + = ++ = −+
= − + = + + = −+
∫∫∫
∫∫∫
:Trignometric Substitutiion
θ
θ
22 22
22 22
22 22
Let tan , sec
Let sin , cos
Let sec , tan
xa xa xaa
ax xa axa
xa xa xa a
θθ
θθ
θθ
+ = +=
− = −=
− = −=
: ln ln ln ln ln ln ln ln
P
A
B
AB A B A B A P A=+=− =Properties of Logarithm
Differentiation
Integration
222
cot cot sec tan csc cot u du u u C u du u C u du u C=−−+ = + =−+
∫∫∫
[ ] [ ]
1 ln log ln
ln
n n uu uu
b
d d ud u d d
cu cnu u u u e e u b b u b
dx dx u dx u b dx dx
−
′′
′ ′′
= ⋅ = = = ⋅ = ⋅⋅
