Page 42 - TUTORIAL_MAT_IPS_K11-2

INTEGRAL FUNGSI ALJABAR

JAWABAN
2
1. ∫(2 − 3) = ∫ 4 − 6 + 9 = 4 2+1 − 6 1+1 + 9 + =
2
2+1 1+1
4 3 2
− 3 + 9 +
3

5
2
2. ∫ 2 − 3 + + 2 = 2 5+1 − 3 4+1 + 1 2+1 + 2 + =
4
1+5 1+4 1+2
1 3 1
6
5
3
− + + 2 +
3 5 3

1
2
3
2
3. ∫ + − 7 = 1 3+1 + 2 2+1 − 7 1+1 + =
3 5 3(1+3) 5(1+2) 1+1
1 2 7
2
4
3
+ − +
12 5 2

2
2
4. ∫ 3 − + 11 = ∫ 2 −2 − + 11 = 2 −2+1 − 2 ln| | + 11 + =
2 1+(−2)
−2 −1 − 2 ln| | + 11 +

1
5 3 1 1 3.5.2 1 1 1 1
5. ∫ √√√ = ∫ ( ) = ∫( −1 )30 = ∫ − 30 = 1 − +1 + =
30
1+(− )
30
30 29
30 +
29

6. ∫(3 + 7) =
6
′
Misal : = 3 + 7 → = 3 → = 3 → =
3
7
6
7
∫(3 + 7) = ∫ 6 = 1 6+1 + = 1 + = 1 (3 + 7) +
3 3(6+1) 21 21
Cara cepat:
6
7
∫(3 + 7) = 1 (3 + 7) 6+1 + = 1 (3 + 7) +
3(1+6) 21

2 1 2 7 9
7. ∫(5 − 1)7 = 2 (5 − 1)7 +1 + = (5 − 1)7 + (cara cepat).
5(1+ ) 45
7

1
8. ∫(3 − 7 ) −2 = 1 (3 − 7 ) −2+1 + = (3 − 7 ) −1 + (cara cepat).
−7(1+(−2)) 7

3
4
9. ∫ 2 (3 + 5) =
3
3
′
3
4
Misal : = 3 + 5 → = 12 → = 12 → =
3 12 3
4
4
3
4
3
4
3 3
∫ 2 (3 + 5) = ∫ 2 = ∫ = 1 + = 1 (3 + 5) +
12 3 6 24 24
Cara cepat :
4
4
4
3
3
4
∫ 2 (3 + 5) = 2 (3 + 5) 3+1 + = 1 (3 + 5) +
3.4.(1+3) 24

‘LEARNING IS FUN’ 41