MATH:Equation of curve passing

2. dy/dx = 6x - 3

y = S (6x - 3) dx = 3x^2 - 3x + C

For the curve passes through (3,1)

1 = 3(3)^2 - 3(3) + C

C = -17

So, the equation of the curve: y = 3x^2 - 3x - 17


3.a. dy/dx = 4e^3x

y = S 4e^3x dx = (4/3)e^3x + C

For the curve passes through (0,8)

8 = (4/3)e^0 + C

C = 20/3

Equation of the curve: y = (4/3)e^3x + 20/3