Final answer:
To evaluate the definite integral involving trigonometric functions, simplification using trigonometric identities is beneficial before proceeding with the computation. The result can be verified graphically to represent the area under the curve, equivalently the work done.
Step-by-step explanation:
The student's question relates to evaluating a definite integral and verifying the result using a graphing utility. When given an integral involving trigonometric functions such as sin and cos, we can make use of certain identities or properties to simplify the computation. As mentioned, the average value over a complete cycle for cos² is the same as for sin² due to the phase difference. This allows us to evaluate the integral more easily. We can then check our results with a graph by showing the area under the curve, which represents the work done. The graphical representation can be carried out with a graphing calculator or software, aligning with the provided instructions to verify the definite integral.
For example, if the integral in question is ∫(8 − 8 sin²), one could use the identity that sin²(x) + cos²(x) = 1 to rewrite and simplify the integral before computing it.