[ itex ]\sqrt{\pi}[ /itex ] - omit the extra spaces.8point1 said:Homework Statement
Find the average value of the function u(x)= 10xsin(x2) on the interval [0, ∏1/2]
(Sorry, I can't figure out how to make the square root symbol)
I get the same thing. Good work!8point1 said:Homework Equations
The Attempt at a Solution
For the integral of u(x), I got -5cos(x2)
I substituted 0 and ∏1/2 and got 10.
then I multiplied by 1/b-a which was 1/∏1/2
making my final answer 10/∏1/2
The average value of a function is the average height of the graph of the function over a given interval. It represents the overall trend or behavior of the function over that interval.
To calculate the average value of a function, you need to first find the integral of the function over the given interval. Then, divide that integral by the length of the interval. This will give you the average value of the function over that interval.
The average value of a function is significant because it can give you a general understanding of the behavior of the function over a specific interval. It can also be used to approximate the exact value of the function at a particular point.
Yes, the average value of a function can be negative. This means that the function has a negative overall trend or behavior over the given interval.
The average value of a function is related to the mean value theorem by representing the slope of the secant line between two points on the graph of the function. This slope is equal to the derivative of the function at a specific point, as shown by the mean value theorem.