Master J said:
...It should be zero in both cases, try showing us what you are doing when you integrate it over x first...The average value of a function over a given interval is the average output or y-value of that function over that interval. It is calculated by taking the integral of the function over the interval and dividing it by the length of the interval.
To calculate the average value of a function, you first need to find the integral of the function over the given interval. Once you have the integral, divide it by the length of the interval. The result is the average value of the function over that interval.
The average value of a function is important because it gives us a single value that represents the overall behavior of the function over a given interval. This can be useful in many applications, such as calculating average speed or average temperature over a period of time.
Yes, the average value of a function can be negative. This can happen if the function has both positive and negative values over the given interval, and the integral of the function over that interval is negative. It is important to consider the sign of the average value when interpreting its meaning.
The average value of a function is related to the mean value theorem in that it represents the y-value where the function intersects its average line. The mean value theorem states that at some point within the interval, the function will have the same slope as the average line. This point is known as the mean value or average value of the function.