without evaluating the integral, is the derivative of the function $\displaystyle \int_{2}^{x} e^{t^{2}-2} dt$ just $\displaystyle e^{t^{2}-2}$?
Thanks in advance for any assistance recieved
Hey ajj86,
First I gotta say, you've been very helpful within the period of 20mins, more than some others on this forum have been in 20days.
MMM, I believe that you are implying the fundamental theorm of calculus whilst using antidifferentiation techniques aka finding the area under graph aka evaluating the integral...? I'm aware it would be a more perfect answer (can u get more perfect than perfect?), but the question strictly states that i must: "Without evaluating the integral, find F'(x) where F(x) = $\displaystyle \int_{2}^{x} e^{t^2-2} dt$" so having said that would $\displaystyle e^{t^2-2}$ be the answer?
Thank you
tsal15
Tsal15, I apologize for not replying last night. I'm not trying to take the easy way out, but I think this might give a better explanation than I can give:
Calculus Facts: Derivative of an Integral
Let me know what you think.
Wikipedia actually has a pretty non-analysis friendly version. Look here
Fundamental theorem of calculus - Wikipedia, the free encyclopedia