# 《步步高学案导学设计》2013-2014学年高中数学苏教版选修2-2【备课资源】152定积分-文档资料_图文

1.5.2

1.5.2

1..

2..

.

1.5.2

1. f(x)[ab]

[ab] n x(x

bn a) x1x2...xi...

xn. Snf(x1)xf(x2)x...f(xi)xi...f(xn)x

x0( n)SnS() S

f(x)[ab]

Sbaf(x)dx f(x) [ab] a b .

1.5.2

2. baf(x)dx

[ab] x . ( x

x )

1.5.2

1

.

""

.

2 baf(x)dx?
baf(x)dx (). baf(x)dx [ab] .

1.5.2

1 abkdxk(ba).

f(x)k

ax0<x1<...<xi1<xi<...<xnb.

[ab] n [xi1xi](i1,2...n)

i(i1,2...n)

in1f(i)xin1kbn ak(ba)

n bakdxk(ba).

[xi1xi]i i.

1.5.2

1 21(1x)dx.

(1)[1,2] n 1in 11ni

(i1,2...n) x1n.

(2)1in 11ni i1in 1(i

1,2...n) f(i)11in 12in 1

n

n

f(i)x

i1

i1

(2in 1)1n

n

i1

2nin21 2nnn12[ 012

...(n1)]

2n12nn212n2n1.

(3)nn f(i)x52. i1

21(1x)dx52.

1.5.2

1.5.2

1 [ab] f(x)

f(x)0 baf(x)dx

f(x)0 baf(x)dx

xaxb(a<b)y0 yf(x)

.

1.5.2

2 f(x)[ab] f(x)0 baf(x)dx f(x)

[ab] f(x)0

x ().

bn a>0f(i)0

f(i)bn a0. abf(x)dx0

baf(x)dxS.

1.5.2

f(x)[ab] baf(x)dx x

f(x) xaxb(ab)

( x x ).()

baf(x)dxS1S2S3.

1.5.2

2

(1)3 3

9x2dx(2)31(3x1)dx(3)

2

sin xdx.

2

(1) y 9x2

3

S1232.

3 3

9x2dx92.

(2) x1x3y0 y

3x1

31(3x1)dx x1x3 y0 y3x1 x

x

1.5.2

31(3x1)dx

12(313)(331)12(131)2

5302316.

(3) ysin x x[22]

2 2

sin

xdx0.

.

1.5.2

2 (1)1 1xdx(2)20cos xdx(3)11|x|dx.

(1)(1)1 1xdxA1A10.

(2)(2)20cos xdxA1A2A30.

(3)(3)A1A21 1|x|dx2A12121.

(A1A2A3 )

1.5.2

1. abf(x)dx ________.

f(x)[ab] i

f(x)[ab] i

f(x) i [ab]

f(x)[ab] i

1.5.2

2.

10xdx__>______10x2dx

20 4x2dx___<_____202dx.

3. 31(3)dx____6____.

4. 2 cos xdx1 x0xf(x)sin x x

0

____2____.

0sin

xdx2

2 0

cos

xdx2.

1.5.2

1.

n
abf(x)dx
i1

bn af(i).

2.""

.

3..