Question

Bantuin dong yang pintar mtk: )
hasil dan caranya

Answer 1

1a. ∫(2x+3)(3x-2) dx
= ∫ (6x² + 5x - 6) dx
= 2x³ + ⁵/₂ x² - 6x + c

b. ∫ (3 - 2√x)² dx = ∫ 9+ 4x - 12√x dx  = ∫ 9 + 4x - 12x¹/² dx
= 9x + 2x² - 8 x³/² +c
= 9x + 2x² = 8x√x + c

2a) ∫ (3x - 2x³)/(x) dx
= ₀¹∫ (3x- 2x³)(x⁻¹) dx = ₀¹∫ 3 - 2x² dx
= 3x - 2/3 x³]¹₀
= 3(1) - 2/3(1)
= 3 - 2/3
= 7/3

b. ₁²∫ 12 - 4x + x² dx
= 12x - 2x² + 1/3 x³]²₁
= 12(1) - 2(3) + 1/3(7)
= 12-6+7/3
= 6+7/3
= 15/3

3a ₋₁⁴∫ (2x+1) dx = x² + x]⁴₋₁ = (16 -1)+ (5) = 20
b. ₀²∫ (2x+1)²- (2x+1) dx =
= ₀² ∫4x²+4x+1 -2x -1 dx
= ₀²∫ 4x²+ 2x dx
= 4/3 x³ + x²]²₀
= 4/3(8) + 4
= 32/3 + 4
= 44/3

4. f'(x)= mx - 4
f '(1) = 2 --> m - 4 = 2
m = 4+2
m = 6

f '(x) = 6x - 4
f(x) = ∫f'(x)  =  ∫(6x - 4) dx = 3x² - 4x +c

f(-1) = 3 --> 3(-1)² -4(-1) +c = 3
3 + 4 +c = 3
c= -4

f(x) = 3x² - 4x - 4

b) ∫fx)  dx = ∫ 3x² - 4x - 4 dx 
= x³ - 2x² - 4x + c

x+1 dx 
= x² + x]²₁
= (4-1)