Set up a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) = 5

Solution:

Given, the function is f(x) = 5

We have to set up a definite integral that yields the area of the region given in the figure.

If f is continuous and non-negative on the closed interval [a,b], then the area of the region bounded by the graph f, the x-axis and the vertical lines x = a and x = b is given by

\(Area=\int_{a}^{b}f(x)dx\)

From the graph, we can compute a = 0 and b = 4

Now, the area of the region can be computed as,

\(Area=\int_{0}^{4}5(x)dx\)

Therefore, the area is \(\int_{0}^{4}5(x)dx\)

Set up a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) = 5

Summary:

The definite integral that yields the area of the region using interval notation is \(\int_{0}^{4}5(x)dx.\)