Integration and area under a curve

Integration reverses differentiation

∫ axⁿ dx = axⁿ⁺¹ ÷ (n + 1) + c (n ≠ -1)

Example: ∫(6x² + 4x) dx = 2x³ + 2x² + c.

Finding c

If you know a point on the curve, substitute it to find c.

Example: dy/dx = 2x and the curve passes through (1, 5): y = x² + c → 5 = 1 + c → c = 4.