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Hello! I have a function ##f(t)## such that ##\int_a^b{f(t)dt}=f_0##. Is there a way to calculate (or bring it to a simpler form) ##\int_a^b{f(a)e^{t}}dt##? Thank you!
As written, ##\int_a^b{f(a)e^{t}}dt = f(a)[e^b - e^a]##.Hello! I have a function ##f(t)## such that ##\int_a^b{f(t)dt}=f_0##. Is there a way to calculate (or bring it to a simpler form) ##\int_a^b{f(a)e^{t}}dt##? Thank you!
Ah sorry, the questions should be about ##\int_a^b{f(t)e^{t}}dt##As written, ##\int_a^b{f(a)e^{t}}dt = f(a)[e^b - e^a]##.
It should be ##f(t)##. It is not an exercise, it is something obtained from a physics experiment, but I would say that yes, the function is differentiable. I can't say that I had many ideas, I was hoping there is probably some formula I don't know about that can be applied, as there is not much to do here with basic integration techniques.May i ask : does the exercise say that ##f(t)## is differentiable? the second integral contains##f(a)##?or perhaps it is ##f(t)##? what is your effort so far?
I don't think the integral can be evaluated without knowing more about f(t).Ah sorry, the questions should be about ##\int_a^b{f(t)e^{t}}dt##