The Riemann sum, the limit as the maximum of delta x sub i goes to infinity of the summation from i equals 1 to n of f of the quantity x star sub i times delta x sub i , is equivalent to the limit as n goes to infinity of the summation from i equals 1 to n of f of the quantity a plus i times delta x, times delta x with delta x equals the quotient of the quantity b minus a and n.
Write the integral that produces the same value as the limit as n goes to infinity of the summation from i equals 1 to n of the product of the quantity 2 plus 3 times i over n and 3 over n.

Question

The Riemann sum,  the limit as the maximum of delta x sub i goes to infinity of the summation from i equals 1 to n of f of the quantity x star sub i times delta x sub i  , is equivalent to the limit as n goes to infinity of the summation from i equals 1 to n of f of the quantity a plus i times delta x, times delta x with delta x equals the quotient of the quantity b minus a and n. 
Write the integral that produces the same value as the limit as n goes to infinity of the summation from i equals 1 to n of the product of the quantity 2 plus 3 times i over n and 3 over n.

anonymous · Answer

https://gyazo.com/4a2702de2f727a0265591e6cfd66d3a9 @jim_thompson5910

anonymous · Answer

Same rules correct?

jim_thompson5910 · Answer

do you see what the value of 'a' is?

anonymous · Answer

a=2 b=5

jim_thompson5910 · Answer

good

jim_thompson5910 · Answer

now do you see what f(x) must be?

anonymous · Answer

It should be just x
Final answer should be D

jim_thompson5910 · Answer

I can't see your answer choices, but you'll find that

a = 2
b = 5
f(x) = x

so

$$\Large \lim_{n \to \infty}\sum_{i=1}^{n}\left(2+\frac{3i}{n}\right)*\frac{3}{n} = \int_{2}^{5}x dx$$

anonymous · Answer

https://gyazo.com/f9c6a5061ff442c9b97d4c357dd71289 :)

jim_thompson5910 · Answer

yep it's D

anonymous · Answer

Is it cool if I just post two other questions here so you can just check them? Instead of making other questions?

jim_thompson5910 · Answer

sure

anonymous · Answer

https://gyazo.com/b78cff91955b504f923a0d1e029f56dd https://gyazo.com/af655f0b48727eebe89ad8bbfec61f24

jim_thompson5910 · Answer

just as long as it doesn't get too cluttered

anonymous · Answer

If either one is wrong, I'll make a new question.

jim_thompson5910 · Answer

They're both correct. Nice job

anonymous · Answer

Appreciate it man

jim_thompson5910 · Answer

no problem