Integral Calculus Problem Example 1

Description:

Problem

The change in a function y and the independent variable x are related as dy/dx = x³. Find y as a function of x.

Solution

We know from the definition of Indefinite Integration that for any function y = F(x),

If, dy/dx = f(x)

Then ∫ f(x) . dx = y + c = F(x) + c [c ∈ constant of integration]

Therefore, for dy/dx = x³,

dy = x³ . dx

y = ∫ x³ . dx

y = x⁴/4 + c