Question

In Exercises \(7-12,\) evaluate the integral. $$\int_{-2.1}^{3.4} 0.5 d s$$

Short answer

The integral evaluates to \(2.75\).

Step-by-step solution

Identify the type of integral

The integral we are dealing with is a definite integral over a constant function. The basic theorem that states that the integral of a constant over the interval \([a, b]\) is equal to that constant multiplied by the size of the interval can be put to use here.

Calculate the size of the interval

Subtract the lower limit of integration from the upper limit: \(3.4 - (-2.1) = 5.5\). So, the size of the interval is \(5.5\).

Evaluate the integral

Finally, the value of the integral is equal to the constant (0.5 in this case) multiplied by the size of the interval. So the value of the integral will be \(0.5 * 5.5 = 2.75\).