1. The problem is to understand how to compute an integral, which is a fundamental concept in calculus used to find areas under curves, among other things. 2. The integral of a function $f(x)$ with respect to $x$ is denoted as $$\int f(x)\,dx$$ and represents the antiderivative or the area under the curve of $f(x)$. 3. The basic rules include: - The integral of a constant $c$ is $$\int c\,dx = cx + C$$ where $C$ is the constant of integration. - The power rule for integration: $$\int x^n\,dx = \frac{x^{n+1}}{n+1} + C$$ for any real number $n \neq -1$. 4. To compute an integral, identify the function type and apply the appropriate rule or method (substitution, integration by parts, partial fractions, etc.). 5. For example, to integrate $$\int x^2\,dx$$: - Apply the power rule with $n=2$: $$\int x^2\,dx = \frac{x^{2+1}}{2+1} + C = \frac{x^3}{3} + C$$ 6. Always add the constant of integration $C$ because integration is the inverse of differentiation and derivatives of constants are zero. This explanation provides the foundation for computing integrals.