The changes in a function y and the independent variable x are related as dy/dx= x2 . Find y as a function of x.

Sol. The change in a function of y and the independent variable x are related as dy/dx = x2 ⇒ dy = x2 dx ∫▒□(24&dy) = ∫▒x2 dx ⇒ y = x3/ 3 + c ∴ y as a function of x is represented by y = x3/3 + c