## anonymous 3 years ago Im doing a problem at the moment and im stuck its a right riemann sum problem, equation and how far i got posted below

1. anonymous

$\int\limits_{3}^{0} (2x^2 + x +3) dx$ $\Delta x = -3/n$ $x_{k} = 3 + -3k/n$ $f(x_k) = (3+ -3k/n)^2 - (3 + -3k/n) +1$

2. anonymous

im not sure where to go from there

3. anonymous

*

4. anonymous

I think you'd be better off using: $\huge \int\limits_{a}^{b} f(x) dx = -\int\limits_{b}^{a} f(x) dx$ at the start

5. anonymous

then $f(c _{k}) = 2*k^2 *\Delta x ^3 + k*\Delta x^2 + 3 \Delta x$

6. anonymous

and $S _{n} = 2 \Delta x ^3 \sum_{}^{} k^2 + \Delta x^2 \sum_{}^{} k +3 \Delta x$

7. anonymous

so if be better of making the original equation negative then using that formula to find the equation

8. anonymous

a bit easier, yes... that's probably why they gave it to you in the form that they did... so you could make the easy simplification

9. anonymous

you got it from here?

10. anonymous

yea i think so i think what confuses me the most is 3+(-3k/n)

11. anonymous

do what I did before you sub.s in 'delta x = b/n'

12. anonymous

$2 * (3+ \frac{ -3k }{ n }^2) * \frac{ -3 }{ n }^3 + (3+ \frac{ -3k }{ n }) * \frac{ -3 }{ n } + 3\frac{ -3 }{ n }$ is this what im looking for or do does k = 1

13. anonymous

start at x=0... move delta x to the right... what's the height of the rectangle you'd draw there?

14. anonymous

|dw:1354238714258:dw|

15. anonymous

height is f(delta x) width is delta x area is f(delta x) * delta x which is (2*(delta x)^2 + delta x +3))*delta x

16. anonymous

|dw:1354238854668:dw|

17. anonymous

next step: go another 'delta x' to the right height is 2*(2*delta x)^2 + 2*delta x +3 width is delta x area is (2*(2*delta x)^2 + 2*delta x +3)*delta x

18. anonymous

so the sum of areas is going to look like: (2*(k*delta x)^2 + k*delta x +3)*delta x

19. anonymous

2*k^2*(delta x)^3 + k*(delta x)^2 +3*delta x

20. anonymous

summing from k=1 to n

21. anonymous

that's the sum I wrote above

22. anonymous

oh alright, thanks i appreciate the help!

23. anonymous

does that make sense?

24. anonymous

Yeah it does, im trying to work through the problem. ill have an answer soon enough though

25. anonymous

still there?

26. anonymous

I didn't write the last term on the summation properly

27. anonymous

it should be:$\Delta x \sum_{k=1}^{n} 3$

28. anonymous

so$S _{n} = 2(\Delta x)^3\sum_{k=1}^{n} k^2 + (\Delta x)^2 \sum_{k=1}^{n} k +\Delta x \sum_{k=1}^{n} 3$

29. anonymous

oh ok, thats makes more sense now

30. anonymous

Its either 0 or -6 i think 0 because n = 3, am i correct?

31. anonymous

it's -63/2

32. anonymous

n is the number of divisions in the partition... you find the sum above (in terms of n) ... you sub.s in b/n for delta x and then you take the limit as n->infinity

33. anonymous

then use b=3 (the interval length) and finally, make the whole result negative ( due to the simplification we did at the very beginning)