Integrals :)

[shiditso]

Evaluate the following limit:

lim?(n??)??_(i=1)^n (7/n ?((1+7i/n) ))

I am pretty sure I need to get an anti-derivative, but get lost somewhere int he process

 

[galactus]

Is this what you mean?:

$\displaystyle \lim_{n\to \infty}\sum_{i=1}^{n}\frac{7}{n\left(1+\frac{7i}{n}\right)^{\frac{1}{3}}}$

If so, this is a Riemann sum. Yes, you are correct. Integration is in order.

It is a Riemann sum with subinterval length $\displaystyle \frac{7}{n}$

$\displaystyle x_{i}=\frac{7i}{n}$

$\displaystyle \int_{0}^{7}\frac{1}{(1+x)^{\frac{1}{3}}}dx$