## CalcDerp102 2 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. CalcDerp102

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

2. CalcDerp102

im not sure where to go from there

3. Algebraic!

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4. Algebraic!

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. Algebraic!

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

6. Algebraic!

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

7. CalcDerp102

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

8. Algebraic!

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. Algebraic!

you got it from here?

10. CalcDerp102

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

11. Algebraic!

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

12. CalcDerp102

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

13. Algebraic!

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

14. Algebraic!

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15. Algebraic!

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. Algebraic!

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17. Algebraic!

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. Algebraic!

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

19. Algebraic!

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

20. Algebraic!

summing from k=1 to n

21. Algebraic!

that's the sum I wrote above

22. CalcDerp102

oh alright, thanks i appreciate the help!

23. Algebraic!

does that make sense?

24. CalcDerp102

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

25. Algebraic!

still there?

26. Algebraic!

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

27. Algebraic!

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

28. Algebraic!

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. CalcDerp102

oh ok, thats makes more sense now

30. CalcDerp102

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

31. Algebraic!

it's -63/2

32. Algebraic!

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. Algebraic!

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