Maklum aja belajar online gimana mau masuk ke otakintinya ya tolongin bro :V

Maklum aja belajar online gimana mau masuk ke otakintinya ya tolongin bro :V

Penjelasan dengan langkah-langkah:

no. 1

∫ (3x² + 2x – 4) dx

= 3/(2 + 1) x^(2 + 1) + 2/(1 + 1) x^(1 + 1) – 4x + c

= 3/3 x³ + 2/2 x² – 4x + c

= x³ + x² – 4x + c

no. 2

₀∫² (3x² – 8x + 5) dx

= (x³ – 4x² + 5x) ]²₀

= (2³ – 4(2)² + 5(2)) – (0³ – 4(0)² + 5(0))

= (8 – 16 + 10) – 0

= 2

no. 3

p > 0 dan

${₁∫}^{p} (2x - 3)dx : = : 12$

$({x}^{2} - 3x){]}^{p}₁ = 12$

((p)² – 3(p)) – (1² – 3(1)) = 12

p² – 3p – (1 – 3) = 12

p² – 3p + 2 – 12 = 0

p² – 3p – 10 = 0

(p + 2)(p – 5) = 0

p = -2 atau p = 5

Karena p > 0, maka nilai p yang memenuhi adalah 5

no. 4

∫ 12x(x² – 3)⁵

= 12x . 1/2x . 1/6 . (x² – 3)⁶ + c

= (x² – 3)⁶ + c

no. 5

∫ 6x√(4x – 3) dx ➡ ∫ 6x(4x – 3)^½ dx

misal :

u = 6x ➡ du = 6 dx

dv = (4x – 3)^½ ➡ v = 1/6(4x – 3)^3/2

maka :

u.dv = u.v – ∫ v.du

u.dv = 6x(1/6(4x – 3)^3/2) – ∫ 1/6(4x – 3)^3/2 . 6 dx

u.dv = x(4x – 3)^3/2 – ∫ (4x – 3)^3/2 + c

u.dv = x(4x – 3)^3/2 – 1/10(4x – 3)^5/2 + c

Semoga Bermanfaat