EXAMPLE 2. Calculate the line integral

$$
\int_{L}(x-y) d l
$$

where $L$ is the line segment from point $A(0,0)$ to point $B(4,3)$.
## Solution.

1. In this case, the equation of the line is $y=3 x / 4 \quad(0 \leq x \leq 4)$ and, consequently, $y^{\prime}(x)=3 / 4$ and $d l=5 / 4 d t$.
2. Substitute these results into formula (1') and compute the definite integral:

$$
\int_{L}(x-y) d l=\int_{0}^{4}\left(x-\frac{3}{4} x\right) \frac{5}{4} d x=\frac{5}{2}
$$

Answer. $\int_{L}(x-y) d l=\frac{5}{2}$.