Evaluate the definite integral. Use a graphing utility to verify your result.0−1(2x − 7) dx

To evaluate the definite integral ∫ from 0 to -1 (2x - 7) dx, follow these steps:

1. Find the antiderivative of the function (2x - 7). The antiderivative of 2x is x² and the antiderivative of -7 is -7x. So, the antiderivative of (2x - 7) is x² - 7x.

2. Apply the Fundamental Theorem of Calculus, which states that the definite integral of a function from a to b is equal to the antiderivative at b minus the antiderivative at a. In this case, a is 0 and b is -1.

3. Substitute these values into the antiderivative: ((-1)² - 7*(-1)) - ((0)² - 7*0) = (1 + 7) - (0) = 8.

So, the value of the definite integral ∫ from 0 to -1 (2x - 7) dx is 8.

To verify this result using a graphing utility, you can graph the function (2x - 7) and use the utility's integral function to find the area under the curve from 0 to -1. The result should be the same.