In this problem you will calculate the area between and the -axis over the interval using a limit of right-endpoint Riemann sums:

Express the following quantities in terms of , the number of rectangles in the Riemann sum, and , the index for the rectangles in the Riemann sum.

  1. We start by subdividing into equal width subintervals each of width . Express the width of each subinterval in terms of the number of subintervals .

  2. Find the right endpoints of the first, second, and third subintervals and express your answers in terms of .
    (Enter a comma separated list.)

  3. Find a general expression for the right endpoint of the th subinterval , where . Express your answer in terms of and .

  4. Find in terms of and .

  5. Find in terms of and .

  6. Find the value of the right-endpoint Riemann sum in terms of .

  7. Find the limit of the right-endpoint Riemann sum.

You can earn partial credit on this problem.