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Lesson: Right Endpoint Riemann Sum

Worksheet • 10 Questions

Q1:

Let 𝑓 ( π‘₯ ) = 3 2 π‘₯ over the interval 1 ≀ π‘₯ ≀ 5 . Evaluate the Riemann sum of 𝑓 using four subintervals and right endpoint sample points, giving your answer to six decimal places.

Q2:

Let 𝑓 ( π‘₯ ) = 1 2 π‘₯ over the interval 1 ≀ π‘₯ ≀ 2 . Evaluate the Riemann sum of 𝑓 using four subintervals and right endpoint sample points, giving your answer to six decimal places.

Q3:

Given 𝑓 ( π‘₯ ) = 2 π‘₯ βˆ’ 5 and βˆ’ 6 ≀ π‘₯ ≀ 4 , evaluate the Riemann sum for 𝑓 with five subintervals, taking sample points to be right endpoints.

Q4:

Given 𝑓 ( π‘₯ ) = 2 π‘₯ βˆ’ 1 and βˆ’ 3 ≀ π‘₯ ≀ 2 , evaluate the Riemann sum for 𝑓 with five subintervals, taking sample points to be right endpoints.

Q5:

Given 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 3 and βˆ’ 3 ≀ π‘₯ ≀ 2 , evaluate the Riemann sum for 𝑓 with five subintervals, taking sample points to be right endpoints.

Q6:

Approximate the integral ο„Έ ο€Ή 3 π‘₯ βˆ’ 5 π‘₯  π‘₯ 2 βˆ’ 2 2 d using a Riemann sum with right endpoints. Take 𝑛 to be 8.

  • A 2 3 2
  • B βˆ’ 6 3 4
  • C βˆ’ 2 3 2
  • D 6 3 4
  • E 4 3 2

Q7:

Approximate the integral ο„Έ ο€Ή π‘₯ βˆ’ 4 π‘₯  π‘₯ 5 3 2 d using a Riemann sum with right endpoints. Take 𝑛 to be 8.

  • A 2 7 1 6
  • B βˆ’ 2 1 3 2
  • C βˆ’ 2 7 1 6
  • D 2 1 3 2
  • E βˆ’ 5 1 6

Q8:

The table gives the values of a function obtained from an experiment. Use them to estimate ο„Έ 𝑓 ( π‘₯ ) π‘₯    d using three equal subintervals with right endpoints.

π‘₯ 3 7 11 15 19 23 27
𝑓 ( π‘₯ ) βˆ’ 2 . 6 βˆ’ 1 . 4 βˆ’ 0 . 7 0.8 2.3 3.4 4.8

Q9:

The table gives the values of a function obtained from an experiment. Use them to estimate ο„Έ 𝑓 ( π‘₯ ) π‘₯    d using three equal subintervals with right endpoints.

π‘₯ 1 5 9 13 17 21 25
𝑓 ( π‘₯ ) βˆ’ 3 . 1 βˆ’ 2 βˆ’ 1 βˆ’ 0 . 4 0.7 2.2 3.1

Q10:

The table gives the values of a function obtained from an experiment. Use them to estimate ο„Έ 𝑓 ( π‘₯ ) π‘₯    d using three equal subintervals with right endpoints.

π‘₯ 1 5 9 13 17 21 25
𝑓 ( π‘₯ ) βˆ’ 3 . 1 βˆ’ 1 . 7 βˆ’ 0 . 4 1.1 2.5 4 5.1
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