estimate the riemann integral

[trickslapper]

f(x)= x^x when x exists (0,1]; 1 when x=0

my professor gave me a hint and said to consider the graph of the piecewise function. at 0 its 1 and also at 1 its 1 and everywhere else its less than 1. So would it be the right idea to estimate f(x) by g(x)=1? f(x) would always be less than or equal to g(x) so the integral of f(x) must be less than equal to the integral of g(x) right?

I'm only asking because this seems too easy...and this class has been anything but easy so where am i messing up ?

 

[tkhunny]

Well, if you think "1" is a reasonable estimate, then go for it. If you need this integral to get your spacecraft to Mars, I'd suggest a much better estimate.

Can you find the minimum value?
If it's 0.999999, or something in that neighborhood, then 1 might be nice.
If it's around, say, 0.6922006275553464, you may wish to revise to a little lower.

Care to take on a Taylor Series? Usually just the first term doesn't get one very far, but maybe.

 

[trickslapper]

thanks for the help tkhunny, estimating it by 1 was what my professor had in mind so i think i'll do that i just didn't believe that it would be that easy.