Question

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

Answer 1

\[\int\limits_{3}^{0} (2x^2 + x +3) dx\]

\[\Delta x = -3/n\]

\[x_{k} = 3 + -3k/n\]

\[f(x_k) = (3+ -3k/n)^2 - (3 + -3k/n) +1\]

Answer 2

im not sure where to go from there

Answer 3

*

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

you got it from here?

Answer 10

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

Answer 11

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

Answer 12

\[2 * (3+ \frac{ -3k }{ n }^2) * \frac{ -3 }{ n }^3 + (3+ \frac{ -3k }{ n }) * \frac{ -3 }{ n } + 3\frac{ -3 }{ n }\]



is this what im looking for or do does k = 1

Answer 13

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

Answer 14

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