Клевчихин - Матан II семестр

ax2 bx

t2x2

2

t2x

2

2 ct

b

c

ctx c

ax

b

ct

x

a

t2

2

a t2

2

dx

c

2t 2 ct b

dt

ct2

2bt 2a c

dt.

a

t2

2

a

t2

2

2

2 ct b

2 ct b

ct2

2bt 2a c

R x, ax2

bx

c

dx

R

, t

c

dt.

2

a

2

a

2

2

a t

t

t

ax2 bx c

a x x1 x x2

a x x1 x x2

x x1

2t2

a x x2

x x1

t2

x

ax2

x1t2

a

t2

dx

2x1t a t2

2t ax2

x1t2

2a x2

x1

t

dt

dt

a

t2

2

a

t2 2

x

x1

ax2

x1t2

x1

a x2

x1

a

t2

a

t2

x

x2

ax2

x1t2

x2

x2

x1 t2

a

t2

a

t2

ax2 x1t2

a x2 x1 2t2

2a x2

x1 t

ax2

R x,

bx

c

dx

R

a

,

dt.

a t2

a t2 2

a t2 2

dx

x

x2

x 1

x2

x 1

x t

t x

x2

x 1

x

x2

x

1

x2

2tx

t2

x

t2

1

dx

2t2

2t

2

dt.

2t

1

2t

1 2

x

tN

N

m

n

dx

N tN 1 dt

xm axn

b p dx

tmN atnN b pN tN 1 dt.

mN nN

p

m 1

axn

b tN

N

0

n

p

tN

1

tN

1

1

b

n

N

b

n

x

tN

1 dt.

, dx

a

na

a

tN

b

m

pN N

tN

b

1

1

n

n

m

n

p

N

1

x

ax

b

dx

t

t

a

na

a

N

tN b

m 1

1

tpN N

1

n

dt.

na

a

pN

N

1

m 1

1

n

m 1

p

n

xn

xm axn

b p dx

xm

np a

bx n p dx.

m

m np

n

n

m 1

m np 1

m 1

p

n

n

n

1

3 x2

xdx

2

1

x 1

x3

2

dx

1

3 x2

1

dx

2

dx

x 2 2 3

1 2x 4x2

x 2

1

3

1

5 x4

4

1

sin x

x2 5 x

dx

2

cos x dx

T

f ; a, b

y

f x

0

x

a

x

b

T f ; a, b

x, y : a x b, y

f x .

y

a; b

a

x1

x2

xn

b

k

xk 1; xk

k

1, . . . , n

x

ξk

ξ1

ξ2

ξ3

ξN

a=x0

x1

x2

x3

. . . b=xn

xk

1; xk

f ξk

n

f ξk xk

xk 1

f ξk xk

xk 1

k

1

a; b

v t

t