Question

evaluate the integral below by interpreting it in terms of areas in the figure. the areas of the labeled regions are a1= 8, a2=3, a3=2 and a4=2 v = \\(\int_{5}^{10} f(x) dx\\) v =

Explanation:

Step1: Identify regions in integral bounds

The integral $\int_{5}^{10} f(x) dx$ covers regions A3 and A4. Regions above the x-axis (A3) contribute positive area, regions below (A4) contribute negative area.

Step2: Calculate the integral value

Assign positive value to A3, negative to A4:
$\int_{5}^{10} f(x) dx = A3 - A4$
Substitute $A3=2$, $A4=2$:
$\int_{5}^{10} f(x) dx = 2 - 2$

Answer:

$0$