1. INTEGRAL
ANTI DEFERENSIAL/ANTI TURUNAN
Turunan Anti Turunan/Integral
f’(x) = 2x F(x) = x2 + 3
F(x) = x2 + 5
F(x) = x2 – 100
F(x) = x2 + c
f’(x) = 3x2 + 2x F(x) = x3 + x2 + 6
F(x) = x3 + x2 - 6
F(x) = x3 + x2 + c
F(x) disebut anti turunan atau integral dari f’(x)
Ditulis dengan notasi F(x) = ∫f’(x) dx

2. Jadi ∫2x dx = x2 + c
∫ 3x2 dx = x3 + c
∫ (3x2 + 2x) dx = x3 + x2 + c
1
∫ x dx = ------ x2 + c = 1/2 x2 + c
1 + 1
1
∫ x2 dx = ------ x3 + c = ⅓ x3 + c
2 + 1
Berapakah ∫ x5 dx
∫ x5 dx = ⅙ x6 + c

3. KAIDAH INTEGRAL
1
1. ∫ xn dx = ------ xn+1 + c
n + 1
2. ∫ k dx = kx + c
3. ∫{f(x) + g(x)} dx = ∫f(x) dx + ∫g(x) dx
1
4. ∫{f(x)n } df(x) = ------- f(x)n+1 + C
n + 1

4. Contoh
Tentukan :
1. ∫ 5x4 dx
2. ∫ (2x2 + 4x -6)dx
3. ∫ (x2 + 3x – 4)(2x + 3)dx
4. ∫ (3x2 + 6x - 9)3 d(x2 + 2x – 3)

5. INTEGRAL TERTENTU
b b
Jika f(x) = F’x), maka ∫ fx dx = F(x)│ = F(b) – F(a)
a a
Dimana b disebut batas atas integral
a disebut batas bawah integral

6. Contoh
Hitunglah :
1
1. ∫ 5x4 dx
0
1
2. ∫ (4x3 + 2x2 6x – 3)dx
-1
3
3. ∫ (3x2 + 6x - 9)d(x2 + 2x – 3)
2

7. Soal 1
Tentukan :
1. ∫ 7x6 dx
2. ∫ (9x2 + 12x - 6)dx
3. ∫ (2x2 + 6x – 8)(2x + 3)dx
4. ∫ (4x2 + 8x - 12)d(x2 + 2x – 3)

8. Soal
Hitunglah :
1
1. ∫ 5x4 dx
-3
3
2. ∫ (4x3 + 2x2 + 6x – 3)dx
-1
2
3. ∫ (4x2 + 8x - 12)d(x2 + 2x – 3)
-2

9. SOAL TUGAS
3
2. ∫ (4x3 + 2x2 + 6x – 3)dx
-3
2
3. ∫ (2x2 + 4x - 6)d(x2 + 2x – 3)
0