Suppose a math class has four equally weighted tests. A student gets 60 on the first test,

Question:

Suppose a math class has four equally weighted tests. A student gets 60 on the first test, 70 on the second, 80 on the third, and 90 on the last.
The average of a step function computed with the definite integral matches the average computed in the usual way. Test this in the following situations by finding the average of the values directly, and then as the integral of a step function.