Integral of (x + 9lnx) as a limit of Riemann sums

[CalcEqualsUgh]

Express the integral as a limit of Riemann sums. Do not evaluate the limit.

11 on top of integral sign
1 on bottom of integral sign (x + 9lnx)dx


Please use only n and i as indices of limit and Riemann sums.

Really lost about the whole Riemann sums thing.

 

[galactus]

Re: Integral as a limit of Riemann sums

\(\displaystyle {\Delta}x=\frac{11-1}{n}=\frac{10}{n}\)

Using the right endpoint method, \(\displaystyle a+i{\Delta}x\):

\(\displaystyle x_{k}=1+\frac{10i}{n}\)

\(\displaystyle {\therefore} \;\ f(x_{k}){\Delta}= \left[\left(1+\frac{10i}{n}\right)+9ln\left(1+\frac{10i}{n}\right)\right]\cdot\frac{10}{n}\)

Remember, that \(\displaystyle \sum_{i=1}^{n}i=\frac{n(n+1)}{2}\)