Question

Sketch the region whose signed area is represented by the definite integral, and evaluate the integral using an appropriate formula from geometry, where needed.

∫⁵₀2dx

Answer 1

The region whose signed area is represented by the definite integral ∫⁵₀2dx, is shown attached.

How to represent the region?

The region whose signed area is represented by the definite integral \
`\int_0^5 2 \, dx\)` is a rectangle with a base from 0 to 5 on the x-axis and a constant height of 2.

The sketch shows this rectangular area in sky blue.

The area of this rectangle, which is the value of the integral, can be calculated using the formula for the area of a rectangle (base × height). In this case, the base is:

5 - 0 = 5

And the height is 2.

Therefore, the area is:
= 5 x 2

= 10