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Well YEAH. You could simply express it as this:buklau said:
It's a valid answer, but I'm not looking for the area. I'm looking for the functions that can derive into f(x)*g(x). It's a bit too ineffable for me.
Since this is an entirely general equation, I would solve this by Integration by Parts. Wiki it if you don't remember the technique (I assume you've been exposed to it if you're being asked to solve this problem).
It's a somewhat long exercise so I don't feel like copying it out here. Integration by parts does assume that f(x) and g(x) are continuous on the interval and differentiable on the interval, so you will need a different technique if that is not the case.
It's a somewhat long exercise so I don't feel like copying it out here. Integration by parts does assume that f(x) and g(x) are continuous on the interval and differentiable on the interval, so you will need a different technique if that is not the case.
What you posted is just the limit definition of an integral, it would amount to the same thing I thought; multiply the functions together, take the integral, evaluate at the initial and final points...unless I am completely forgetting everything calculus related already lol. (reading other posts above mine, it appears I amNotAProdigy said:Well YEAH. You could simply express it as this:buklau said:
It's a valid answer, but I'm not looking for the area. I'm looking for the functions that can derive into f(x)*g(x). It's a bit too ineffable for me.
)
"Biology is just chemistry, chemistry is just physics, physics is just math, and math is just really hard." Quote: My first year chem prof
anyway, you have to do integration by parts
u = f(x) dv = g(x)dx
du = f(x)'dx v = integral of g(x)dx
then you do u*v - integral of (v*du)
so f(x)*g(x) - integral of [g(x)*{f(x)'}]
input and solve
you must still solve with A and B, so
f(x)*g(x)(solved from A to B) - integral (from a to be) of [g(x)*{f(x)'}]
you maybe have to repeat or continue with another technique.
anyway, you have to do integration by parts
u = f(x) dv = g(x)dx
du = f(x)'dx v = integral of g(x)dx
then you do u*v - integral of (v*du)
so f(x)*g(x) - integral of [g(x)*{f(x)'}]
input and solve
you must still solve with A and B, so
f(x)*g(x)(solved from A to B) - integral (from a to be) of [g(x)*{f(x)'}]
you maybe have to repeat or continue with another technique.
your just integrating the product rule, for that problem you use the method of integration by parts. http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/techniques/parts.html
