cba
f
xdx
c
is
a
y
co
sta
t
b
a
f
xdx

c
b
f
xdx
ca
f
xdx
ba
f
x

gxdx

b
a
f
xdx
ba
gxdx
5
fAPCALCULUS
Derivative
b
a
f
xdx
Fxba

Fb

Fa
where
Fxfxdx
a
a
f
xdx

0（fx
odd）
a
a
f
xdx

2a0
f
xdxfxeve

If
fx0o
axbthe

b
a
f
xdx

0
If
fxgxo

axbthe

b
a
f
xdx

b
a
gxdx
Theaveragevalueofafu
ctio
o
a
i
tervalab
fave

b
1
a
b
a
f
xdx
3Thei
fi
itei
tegral
IfFxfxthe
fxdxFxC
Formulas
x
dx

1
1
x
1

C


axdx

1l
a
ax

C
si
xdxcosxC

cosxdxsi
xC

ta
xdxl
cosxCcotxdxl
si
xC

dxarcsi
xC1x2
x21
dx
1x2
arcta
xC
USubstitutio

fgxgxdxsubstitutio
ugxfudu
I
tegratio
byParts
udvuvvdu
6
fAPCALCULUS
Derivative
7
fr