Hello, I am a medical doctor but interested in mathematics and physics. Consider a parabola with its equation y = x2 dy/dx = 2x and dy = 2x.dx If we make small right angled triangles under the parabola with the base dx then the height of the triangles will be dy. The hypotenuse (dh) of the triangles will be dh2 = (dx)2 + (dy)2 dh2 = (dx)2 + (2x.dx)2 dh2 = (dx)2 (1 + 4x2) if we integrate dh it will give us the sum of squares of the small pieces of the curve, which is parabola here (Sh2). Sh2 = ∫ 1 + 4x2.dx2 But I have been told that it is not allowed in calculus to integrate dx squared. Can some one please shed some light on it? Thank you.