# Need Upper Bound of an Integral

Hello everybody,
I need help with a Calculus Problem. Given is a function $f(t)=0,0025t^4-0,14t^3+1,8t^2$
The function describes the sales of a product in it's lifecycle.
The t is given in months and the y units sold in thousands.
The question is, at when point in time (at which exact value for $t$ ) are 750 thousand units sold ($f(t)=750$ ).
My approach was building the antiderivative and setting it equal to 750  ($\int_{0}^{x}f(t)\;\mathrm{d}t = 750$, where x is the boundary (the second x-axis section which is needed to solve the problem))
I tried to solve this but couldn't get a correct result. What would be the proper way to solve it?
(I would want not just the result but how you got there as well)
((I also haven't got much money to offer for this but I think it shouldn't be that demanding))

• Emmadoessomecalc

I should also add, that the answer should be in the Interval [0; 19]. This probably isn't necessary though, since I did a rough graphical approximation and I believe it was somewhere around the 17 months Mark.

• Emmadoessomecalc

(Please replace the commas with dots when doing this, I'm german and we note decimal places with a comma rather than a dot)

• Alessandro Iraci

I think that the amount is quite low for this question, and also that it's poorly stated, since you're asking two separate things. I suppose the original text was in German, but right now it's not clear if f(t) is the amount of goods sold "in the t-th month" or "until the t-th month", and of course the problem is different in the two cases.

• Nirenberg

So f=0.0025t ^4−0.14t^3 +1.8t+8t^2 and it represents the number of units (in thousands) sold between the time 0 and t?

• Nirenberg

Alessandro is right. Please clarify what f(t) represents.

• Alessandro Iraci

Also note that setting the antiderivative of that equal to 750 requires finding a zero of a 5-th degree polynomial, which is impossible to do exactly except in some very special cases. Not sure, but I think it's unlikely that it's one of these cases.

• Emmadoessomecalc

f(t) represents the units sold in t-th month. So if finding the zero to this 5th degree polynomial is likely to be impossible, what is the correct way to do it instead?

• Daniel90

• Emmadoessomecalc

What would be a proper bounty then? I'm new to this platform and if course don't know such things... As I stayed already though, I don't really habe much more to offer. It's fine though. I'm sorry that I can't offer more and will accept the fact that my bounty is too low.

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• Nirenberg