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 1 plus 3 times i over n and 3 over n .

the integral from 1 to 3 of the quantity x plus 1, dx
the integral from 1 to 4 of x, dx
the integral from 1 to 4 of the quantity 3 times x plus 1, dx
the integral from 1 to 3 of x, dx

Answer 1

Hard to say, having to parse all that English, but I'd guess the first one, since that seems to involve 1+x, corresponding to a value of a=1 in the above recitation.

Still, it could be the 3rd one, but the interval [1,4] bothers me.

The description seems to indicate that if you understand the sum=limit equation, it should be clear. I'd say google is your friend here.

Answer 2

I just did this question, the answer is the second one or the integral from 1 to 4 of x, dx