Final answer:
To evaluate the integral ∫|x - 5| dx from 0 to 10, we can interpret it as the area between the curve and the x-axis. Splitting the interval into two parts, we calculate the area of two triangles formed by the function |x - 5|. Adding the areas of the two triangles gives us the total area.
Step-by-step explanation:
To evaluate the integral ∫|x - 5| dx from 0 to 10, we can interpret it in terms of areas. The absolute value function |x - 5| creates a V-shaped graph around x = 5. The integral from 0 to 10 represents the area between the curve and the x-axis within that interval.
Since the function is symmetric around x = 5, we can split the interval into two parts: from 0 to 5 and from 5 to 10. In the first part, the integral becomes ∫(5 - x) dx from 0 to 5, which represents the area of the triangle under the line y = 5 - x. In the second part, the integral becomes ∫(x - 5) dx from 5 to 10, which represents the area of the triangle above the line y = x - 5.
By calculating the areas of the two triangles, we can find the total area between the curve and the x-axis within the interval 0 to 10.