Average Value of a Function
Read this topicExplanations 4
- The average value of a function over a particular interval can be found with an expression involving an integral. Obviously you must know the algebraic function, f(x)f(x)f(x). A…
By Joshua Siktar, Ahaan Rungta
- The average value of a function is the average height of the graph of a function. The average value of a function f(x) over the interval [a,b] is given by the formula fave=1b−a∫…
By Kaila Piscitelli, Alex Federspiel
- An integral is the area under a curve. A definite integral is the area under a curve from one point to another along the x-axis. There is a specific point on the y-axis where if…
By Maya Schwartz, Caroline K
- Say we want to find the average value of the function f(x)=1+x2f(x) = 1 + x^2f(x)=1+x2 on the interval [−1,2].[-1,2].[−1,2]. The average value of a function, or the average heig…
By Noah Libby, Caroline K
Problems 4
- Find the average value of the function y=cosxy = \cos xy=cosx over the interval x∈[−π,π]x \in \left[ -\pi, \pi \right]x∈[−π,π].
- Compute the arithmetic mean of all of the real numbers between 000 and 111.
- Compute the geometric mean of all of the real numbers between 000 and 111.
- Let ℓ\ellℓ be a line of length π\piπ in the plane. Find the expected value of the length of the projection of ℓ\ellℓ along a line in a random direction.