Write the definite integral for the summation:

Question

Answer 1

The numerator in the 3/n (which represents the width of each of n rectangles) is calculated as -> (b-a)/n.

Since k starts at 1,using right hand endpoints, which means 3k/n is what is added to a to get each of the right-hand endpoints

Each x_i (right hand endpoint) is plugged into a function x².

So the definite integral is:∫⁷₄ x² dx.

Check out this page for confirmation:

desmos.com/calculator/kxh1q3oda1

Answer 2

This would be the integral of (4+x)^2 from 0 to 3, as this is the right Riemann sum.