What is the result of evaluating the definite integral ∫ from 0 to 3 of (5) dx?

To evaluate the definite integral from 0 to 3 of the constant function 5, we can use the fundamental theorem of calculus. The integral of a constant ( c ) over an interval ([a, b]) is given by the formula:

[

\int_a^b c , dx = c(b - a)

]

In this case, our constant ( c ) is 5, the lower limit ( a ) is 0, and the upper limit ( b ) is 3. Applying the formula:

[

\int_0^3 5 , dx = 5(3 - 0) = 5 \times 3 = 15

]

Thus, the value of the definite integral is 15. This makes it clear that the integration of a constant over a defined range results in the constant multiplied by the width of the interval, which in this case is 3. Therefore, the correct answer is 15.