Evaluate the integral of x^2 dx.

The integral of x^2 dx is (1/3)x^3 + C, where C is the constant of integration.

To evaluate the integral of x^2 dx, we use the power rule of integration, which states that the integral of x^n dx is (1/(n+1))x^(n+1) + C, where C is the constant of integration. Applying this rule to x^2, we get:

∫ x^2 dx = (1/3)x^3 + C

To check our answer, we can differentiate (1/3)x^3 + C with respect to x using the power rule of differentiation, which states that the derivative of x^n is nx^(n-1). Applying this rule to (1/3)x^3, we get:

d/dx [(1/3)x^3] = (1/3) * 3x^2 = x^2

This confirms that our answer is correct.

In general, when evaluating integrals, it is important to remember the constant of integration, as it can affect the final answer. The constant of integration arises because the derivative of a constant is zero, so any constant added to the antiderivative will not affect the derivative. Therefore, when evaluating integrals, we always include the constant of integration to account for this possibility.