Integrate x3 dx from 2 to 4

We use the power rule for integration, which states that $\int x^n \,dx = \frac{x^{n+1}}{n+1}$.
Here, $n=3$.

$$\int x^3 \,dx = \frac{x^{3+1}}{3+1} = \frac{x^4}{4}$$

The definite integral is evaluated as $F(b) - F(a)$, where $F(x)$ is the antiderivative and $a$ and $b$ are the lower and upper limits, respectively.

$$\int_{2}^{4} x^3 \,dx = \left[ \frac{x^4}{4} \right]_{2}^{4}$$

$$\frac{256}{4} - \frac{16}{4}$$ $$64 - 4$$ $$60$$