Recent content by zillac

Homework Statement Find \int\sqrt{\frac{x}{x^2+2}}dx Homework Equations N/A The Attempt at a Solution Don't know where to start. I tried a few substitution but doesn't yield anything. It seems to be short, so any small hint will be great. Thanks!

I tried using Riemann sums and it will go back to finding the sum of the sequence (\frac{1}{n^{\frac{3}{2}}}\sum^{n}_{i=1}\sqrt{i}) I(n)-I(n-1)~c*(n^(3/2)-(n-1)^(3/2)) will work when alpha is found. So, c = \frac{\sqrt{n}}{n^\frac{3}{2}-(n-1)^\frac{3}{2}} ... =...

Sorry I forget to say that the fundamental theorem of calculus cannot be used, otherwise it is pretty straight forward. Thanks for the quick reply.

Homework Statement Find the asymptotic formula for \sqrt{1}+\sqrt{2}+\sqrt{3}+\sqrt{3}+...+\sqrt{n} in the form of c \ast n^{\alpha} Identify c and alpha. (Do NOT use the fundamental theorem of calculus) Homework Equations Area under curve y = \sqrt{x} in [0, 1] is...