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Integral

3.  f'(x) = 3x - 4
f(x) = ∫ 3x - 4 dx = 3/2 x² - 4x + c
f(-2) = 5
3/2 (-2)² - 4(-2) + c = 5
6 + 8 + c = 5
13 + c = 5
c = - 8
f(x)= 3/2  x²- 4x - 8

4. m = dy/dx = 3x² - 4x + 6
y = ∫ dy/dx =  ∫ 3x² -4x + 6 dx
y = x³ - 2x² + 6x + c
melalui (x,y)= (2, 21)
21 = (2)³ - 2(2)² + 6(2) + c
21 = 8 - 8 + 12 + c
21 = 12 + c
x = 9
y = x³ - 2x² + 6x + c

5. v(t) = 3t² - 2t

s(t) =  ∫ v(t) dt
s(t) =  ∫ 3t² - 2t  dx
s(t) =  t³ - t² + c
s(3)= 9 --> 3³ - 3² + c = 9
27 -9 + c = 9
18 + c = 9
c = - 9

s(t) = t³ - t² - 9