Question

Given that dy/dx = 3x² + 5x + 10 and when x = 2 and y = 3 find an expression for y in terms of x.

Answer 1

\(\int dy = \int (3x^2 + 5x +10)dx\)

\(\therefore y =x^3 + \frac{5x^2}2 + 10x + c\)

\(x = 2, y =3\)

\(\therefore 3 = 8 + 10 + 20 + c\)

⇒ \(c = 3 - 38 = - 35\)

\(\therefore y = x^3 + \frac{5x^2}2 + 10x - 35\)