I need help with integral please

Question

The Riemann sum,  , is equivalent to  with  .

Please write the integral that produces the same value as  .

Options:

1. 
2. 
3. 
4. 

Answer 1

Given:

n

Lim ∑ f (x+i*Δx) Δx

n -> ∞ i=1

Δx = (b-a) / n

Find:

n

Lim ∑ (3+5i)²)/n * 5/n

n -> ∞ i=1

Since Δx = (b-a) / n = 5/n, then (b-a) must equal 5, so we can eliminate choices #2 and #4,

1) b-a = 8-3 = 5

2) b-a = 3-0 = 3

3) b-a = 5-0 = 5

4) b-a = 5-3 = 2

Since f(x) = (3+5i)²)/n

The correct answer is #1:

8

∫ x² dx

3

#3 look almost correct, however what happened to the quantity squared?

5

∫ (3+5x) dx

0