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aakeso1
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Homework Statement
Show that <sin^2(k*r-wt)>= 1/2
Homework Equations
<f(t)>= 1/T integral ( f(t')dt' ) from [t, t+T]
Right, so I use the appropriate identity ( 1-2sin^2(x) ), and carry out the integration?Svein said:Trigonometric identities: You know that [itex]\cos(2x)=\cos^{2}(x)-\sin^{2}(x)=1-2\sin^{2}(x) [/itex]?
aakeso1 said:Right, so I use the appropriate identity ( 1-2sin^2(x) ), and carry out the integration?
Well, I do not know exactly what you mean, but solve the identity for sin2(x) and integrate (for example from 0 to 2π).aakeso1 said:Right, so I use the appropriate identity ( 1-2sin^2(x) ), and carry out the integration?
A time average integral is a mathematical concept used to calculate the average value of a function over a certain period of time. It is represented by the symbol ∫t f(t) dt, where f(t) is the function and t represents time.
Unlike a regular average, which calculates the mean value of a set of data points, a time average integral takes into account the changing value of a function over time. It is often used to analyze systems that have varying behaviors over time.
Time average integrals are commonly used in scientific research to analyze the behavior of complex systems, such as in physics, engineering, and economics. They provide a way to calculate the average value of a function over time, which can help in understanding the overall behavior of the system.
To calculate a time average integral, the function f(t) is first integrated over a specific time interval. The resulting value is then divided by the length of the time interval to get the average value. This process is repeated for multiple intervals to get a more accurate average.
Yes, a time average integral can be negative if the function being integrated has values that are both positive and negative over the given time interval. The negative value indicates that the function spends more time with negative values than positive values over the interval.