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y = x − 2 x − 2 と y = − x +4 で囲まれる面積

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(1)

y = x

2

− 2x − 2

と

y = − x +4

で囲まれる面積

y=x2−2x−2

−2 3

(2)

y = x

2

− 2x − 2

と

y = − x +4

で囲まれる面積

y=x2−2x−2

y=−x+4 まず連立方程式を解いて、交 点の

x

座標を計算する

(3)

y = x

2

− 2x − 2

と

y = − x +4

で囲まれる面積

y=x2−2x−2

y=−x+4 まず連立方程式を解いて、交 点の

x

座標を計算する

x2−2x−2 = −x+4 x2−x−6 = 0

(x+2)(x−3) = 0 x = −2, 3

(4)

y=x2−2x−2 y=−x+4

−2 3

まず連立方程式を解いて、交 点の

x

座標を計算する

x2−2x−2 = −x+4 x2−x−6 = 0

(x+2)(x−3) = 0 x = −2, 3

(5)

y = x

2

− 2x − 2

と

y = − x +4

で囲まれる面積

y=x2−2x−2 y=−x+4

−2 3

∫

範囲の上 範囲の下

(

上の式

−

下の式

)dx

(6)

y=x2−2x−2 y=−x+4

−2 3

∫

範囲の上 範囲の下

(

上の式

−

下の式

)dx

=

∫

3

−2

(

( − x +4)

− (x

2

− 2x − 2) )

dx

(7)

y = x

2

− 2x − 2

と

y = − x +4

で囲まれる面積

∫

3

−2

(

( − x +4) − (x

2

− 2x − 2) )

dx

=

∫

3

−2

( − x

2

+ x +6 )

dx

= [

− 1

3 x

3

+ 1

2 x

2

+6x ]

3

−2

(8)

= [

− 1

3 x

3

+ 1

2 x

2

+6x ]

3

−2

= (

− 1

3 × 3

3

+ 1

2 × 3

2

+6 × 3 )

− (

− 1

3 × ( − 2)

3

+ 1

2 × ( − 2)

2

+6 × ( − 2)

)

(9)

y = x

2

− 2x − 2

と

y = − x +4

で囲まれる面積

= (

− 1

3 × 3

3

+ 1

2 × 3

2

+6 × 3 )

− (

− 1

3 × ( − 2)

3

+ 1

2 × ( − 2)

2

+6 × ( − 2) )

= (

− 27

3 + 9

2 +18 )

− ( 8

3 + 4

2 − 12

)

(10)

y = x

2

− 2x − 2

と

y = − x +4

で囲まれる面積

= (

− 27

3 + 9

2 +18 )

− ( 8

3 + 4

2 − 12 )

= − 27

3 + 9

2 +18 − 8

3 − 4

2 +12

3 2

(11)

y = x

2

− 2x − 2

と

y = − x +4

で囲まれる面積

= (

− 27

3 + 9

2 +18 )

− ( 8

3 + 4

2 − 12 )

= − 27

3 + 9

2 +18 − 8

3 − 4

2 +12

= − 27 − 8

3 + 9 − 4

2 +30

(12)

= − 27 − 8

3 + 9 − 4

2 +30

= − 35

3 + 5

2 +30

= − 70

6 + 15

6 + 180

6

(13)

y = x

2

− 2x − 2

と

y = − x +4

で囲まれる面積

= − 70

6 + 15

6 + 180 6

= 125

6

参照

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