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Jbreezy
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Homework Statement
I have a question can the average value for an integral be negative. I don't see why not just checking.
You know this evalutation f_ave = (1/b-a) ∫ f(x) dx
Homework Equations
thx
Jbreezy said:Homework Statement
I have a question can the average value for an integral be negative.
You know this evalutation f_ave = (1/b-a) ∫ f(x) dx
If the average value of the function is negative, of course!Jbreezy said:Homework Statement
I have a question can the average value for an integral be negative. I don't see why not just checking.
More correctly f_ave = (1/(b-a)) ∫ f(x) dx. What you wrote would normally be interpretedYou know this evalutation f_ave = (1/b-a) ∫ f(x) dx
Of course. Take the simplest example: f(x)= -1 for all x.Homework Equations
thxx
The Attempt at a Solution
The average value for integrals is a numerical value that represents the average of a function over a given interval. It is calculated by dividing the definite integral of the function over the interval by the length of the interval.
The average value for integrals is calculated using the formula: (1/b-a) * ∫f(x)dx from a to b, where a and b are the limits of integration and f(x) is the function being integrated.
The average value for integrals is significant because it represents the average behavior of a function over a given interval. It can provide insight into the overall trend or behavior of a function and is often used in real-world applications such as calculating average velocity or average power.
Yes, the average value for integrals can be negative. This can occur when the function being integrated has both positive and negative values over the given interval, resulting in a net negative average value.
The average value for integrals is used in practical applications such as calculating the average speed of an object, finding the average temperature over a given period of time, or determining the average rate of change of a quantity. It is also used in economics and finance to calculate average revenue or average return on investments.