Matematika Ekonomi.docx

KELOMPOK 9 SUSUNAN : 1. Muhammad Al Fath Pradipta Siwi 2. Anggita Dwitaningrum 3. Wiratni 4. Faishal Farras Atha

1.

(B100180070) (B100180076) (B100180112) (B100180118)

a. ∫(𝟒𝒙𝟕 + 𝟑𝒙) dx 4

=

8

𝑥8 +

3

𝑥8 +

3

1

=

2

𝑥2 + C

2 2

𝑥2 + C

b. ∫(𝟖𝒙𝟑 + 𝟑𝒙) dx 8

𝑥4 +

1

= 2𝑥 4 +

1

=

4

2 2

𝑥2 + C 𝑥2 + C

c. ∫(𝒙𝟒 + 𝟒𝒙) dx = =

2.

1 5 1 5

𝑥5 +

4 2

𝑥2 + C

𝑥 5 + 2𝑥 2 + C

𝟑

a. ∫𝟏 (𝒙𝟒 + 𝟑) dx 3

3

= ∫1 𝑥 4 dx + ∫1 3 dx =

1 5

𝑥 5 ]13 + 3𝑥 ]13

1

1

5

5

= ( (3)5 − =( =

243 5

242 5

−

+6

= 49, 6

1 5

(1)5 ) + (3(3) − 3 (1))

) + (9-3)

𝟑

b. ∫𝟏 (𝟐𝒙𝟑 + 𝟓) dx 5

5

= ∫4 2𝑥 3 dx + ∫4 5 dx 5

2

5

= 𝑥 4 ]4 + 5𝑥 ]4 4

1

1

2

2

= ( (5)4 − = (

625 2

−

256 2

(4)4 ) + (5(5) − 5 (4))

) + (25-20)

= (184, 5 + 5) = 189,5

𝟓

c. ∫𝟐 (𝟐𝒙𝟑 + 𝟒) dx 5

5

= ∫2 2𝑥 3 dx + ∫2 + 4 dx 5

2

5

= 𝑥 4 ]2 +4𝑥 ]2 4

1

1

2

2

= ( (5)4 − = (

625 2

−

16 2

(2)4 ) + (4(5) − 4(2))

) + (20-8)

= (304,5 + 12) = 316,5

3. 𝐷 ≡ 𝑃 𝑆≡

15 − 3𝑋

= 𝑋

𝑃−3

=

−𝑃 = −3 − 𝑋 𝑋 −1 𝑃 =3+𝑋 𝐷=𝑃 15 − 3𝑋 = 3 + 𝑋 12 = 4𝑋 3 = 𝑋 → 𝑋𝑒 𝑋 = 3 → 𝑃 = 15 − 3𝑋 = 15 − 3(3) = 6 → 𝑃𝑒

𝑋

𝐶𝑆 = ∫0 𝑒 𝑓(𝑥) 𝑑𝑥 − 𝑋𝑒 − 𝑃𝑒 3

= ∫0 (15 − 3𝑋 )𝑑𝑥 − 3 ∙ 6 3

3

= ∫0 15 𝑑𝑥 − ∫0 3𝑋 𝑑𝑥 − 18 3 = 15 𝑋 ] − 0

3 2

3 𝑥 2 ] − 18 0 3

3

2

2

= (15(3) − 15(0)) − ( (3)2 − = 45 − 13,5 = 31,5 𝑋𝑒

𝑃𝑠 = 𝑋𝑒 ∙ 𝑃𝑒 − ∫0 𝑓 (𝑥) 𝑑𝑥 3

= 3 ∙ 6 − ∫0 3 + 𝑥 𝑑𝑥 3

3

= 18 − ∫0 3 𝑑𝑥 + ∫0 𝑥 𝑑𝑥

(0)2 ) − 18

3 = 18 − 3𝑥] + 0

3 𝑥2] 2 0 1

1

1

2

2

= 18 − (3(3) − 3 (0)) + ( (3)2 −

(0)2 )

= 18 − (9 + 4, 5) = 18 + 4,5 = 13,5

4. 𝑃 = 15 − 3𝑥

𝑏𝑖𝑙𝑎

𝑝=6 𝑑𝑝

6 = 15 − 3𝑥

𝑑𝑥

= −3

𝑥=3 𝑑𝑥 𝑑𝑝

=−

1 3

−9 = −3𝑥 3=𝑥 Besarnya elastisitas permintaan akan barang ini adalah: 𝑃

Harga :

𝑋

∙

𝑑𝑥 𝑑𝑝

6

= ∙− 3

1 3

6

2

9

3

=− ∙−

besarnya elastisitas akan barang ini adalah bila p : 6 dp dx

x:2

= 1 =>

harga

:

dx dp

p x 6

.

= 1

dx dp

: .1 3

:

6 3