IIIIIIIIIIIIIIIII
x Dx
D
x
Dx
x
x Dx
m
m m
m
m SS
II
Dx
I
= vrr
m
Dt
I
I
I
m
Dx
m m = tva = vlllll
I
Dt®0
Dt
I
IIIIIIIIIIIIIIIII
tva2 = 0
tva > 0
tva3 < 0
m
m
m g x g a
0
m m 0
m m m m m g 0
2
II IIIII I III IIIII IIIIIIIIII
I
IIIIII III I I I
III
f x m F x
F x g f x
m
F1 x g F x C1
II IIIII I III IIII
a a
f x xx = F x + C
ò
f x
f x xx x m
3
II IIIII I III II I
m m
x
n-
xn = nx
xxx = x2
) )
ò
2
xx
xmxx = xm+ m m
ò
m +
xx = m x
ò
x
ò xxx = - x ò xxx = x
f x xx
òa f x xx = a ò
ò x + v - l xx = òxxx + òvxx - òlxx
4
II IIII III IIIII II II II
abb m m n D xl x xl xl 1
m xl
b
n
f x xx = m m0 f xl Dxl
å
ò
Dxl ®
l=
a
n®0
m m xl
xl b m
b
f x xx
ò
a
a aa m
f x y g 0 x g ab x g b
f x xx
a m
b
x m
5
II I IIIII I I IIII
b a
a
f x xx = - f x xx f x xx = 0
ò ò ò
a b a
b l b
f x xx = f x xx + f x xx
ò ò ò
a a l
b b
f x xx
òl × f x xx = l ×ò
a a
b b b b
ò]x x + v x - l x ]xx = òx x xx + òv x xx - òl x xx
a a a a
6
 I I II III I I III
III II
m f x m ab b
x
b
f x xx = b - a × f x
ò
a
f x f x m ab b
III I I I I I II I
IIIIIIIIII II II
f x xx = F x + C
m
ò
b
b
f x xx = F b - F a º F x
ò
a
a
7
 I I
IIIII I IYIIII
r
x r
m
r
r t = x t × x
) ) ) )
xx
r xx
® = v
2 v t = × x = v t × x
) ) ) )
xt
xt
xv
r xv
® = a
3 a t = × x = a t × x
) ) ) )
xt xt
m m m S S x t b v t a t
2
x )t )
t
xx x v× xt ®
xx = vxt
ò ò
x t
0 0
t
x = x0 + vxt x0 = x t0
) )
ò
t0
3
v t
t
xv x a× xt ®
x v = ax t
ò ò
v0 t0
t
v = v0 + axt
v0 = v t0
) )
ò
t0
8
 IIIII III III II I IYIIII II
a x 0b v g
t
m m
x = x0 +
òvxt
t0
xmxx = xm+
ò
m +
t
g t0
x = x0 + v xt
ò
0
t0
òt xt = 0 + t0+ = t
x = x0 + v t - t0
) )
9
 IIIII III IIII II II II I
a x . t0 g 0
t
v = v0 +
òaxt = v0 + at
0
t t
x = x0 +
0
òvxt = x0 + ò)v + at)xt
0 0
2
x = x0 + v0t + at
2
m m
xmxx = xm+
ò
m +
+
òt xt = + t = 2 t2
0
 I I
IIIII IYIIII
r r
r xr r xv
v = a =
xt xt
r r r r
vxt = xr axt = xv
r r
r t v t
t t
r r r r
òvxt = òxr òaxt = òxv
r r
0 r 0 0 v 0
t t
r r r r r r
òvxt = r t - r 0 òaxt = v t - v 0
0
0
t t
r r r r r r
r t = r0 + v t = v0 +
òvxt òaxt
0 0
I III IIII II II II I
I
r
a =
t
t
r r r
v t = v0 +
òaxt
òxt = t
0
0
r r rt
v t = v0 + a
òxt
0
r r r
v = v0 + at
t
r r r
r t = r0 +
òvxt
0
t
r r r r
r t = r0 +
0
ò)v + at)xt
t
0
òtxt = 2 t2
t t
r r r r
0
r t = r0 +
0
òv xt + ò)at)xt
0 0
r r rt rt
r t = r0 + v0
òxt + aòtxt
0 0
r r r r
r = r0 + v0t + at2
2
2
 IIIII IYIIII I
I III IIII II II II I
r
a =
r r r
v = v0 + at
r r r r
r = r0 + v0t + at2
2
m
m
m
a v0
r0.
m m
m m m m m
m
m m
m m m m
r
v =
3