## anonymous one year ago Write the definite integral for the summation

1. anonymous

2. anonymous

@LynFran @mathway @mathmate @jim_thompson5910

3. anonymous

soo im not really sure what to do ....

4. anonymous

@tkhunny @Michele_Laino @ganeshie8 @Hero @nincompoop

5. anonymous

this a simple Riemann sum with uniform partition of the domain of integration; we have here that $$\Delta x=3/n$$ and it looks like we're integratign the function $$x\mapsto x^2$$ by sampling the points $$x_k=4+k\Delta x=4+3k/n$$, so the domain of integration is between $$4$$ and $$4+3=7$$: $$\lim_{n\to\infty}\sum_{k=1}^n (x_k)^2\cdot \Delta x=\int_4^7 x^2\, dx$$

6. anonymous

that actually makes sense, thank you !