# Worksheet: Riemann Sums

In this worksheet, we will practice approximating the area under the curve of a function using right, left, and midpoint Riemann sums.

Q1:

Given that and that , evaluate, to the nearest six decimal places, the Riemann sum for with six subintervals, taking the sample points to be left endpoints.

Q2:

Let over . Using four subintervals and taking midpoints as sample points, evaluate the Riemann sum of to six decimal places.

Q3:

Given and , evaluate the Riemann sum for with six subintervals, taking sample points to be midpoints.

• A5
• B
• C
• D
• E7

Q4:

Let over the interval . Evaluate the Riemann sum of using four subintervals and right endpoint sample points, giving your answer to six decimal places.

Q5:

Given and , evaluate the Riemann sum for with five subintervals, taking sample points to be right endpoints.

Q6:

Use left Riemann sum to approximate the area under the curve of on the interval . Use subintervals with .

• A
• B
• C
• D
• E

Q7:

Use left end point approximation to approximate the area under the curve of on the interval ; use subintervals with .

• A
• B
• C
• D
• E

Q8:

Use a right Riemann sum to approximate the area under the curve of in the interval . Use subintervals with . Approximate your answer to three decimal places.

Q9:

Use a right Riemann sum to approximate the area under the curve of in the interval . Use subintervals with .

• A
• B
• C
• D
• E

Q10:

Use left Riemann sum to approximate the area under the curve of on the interval ; use subintervals with .

• A
• B
• C
• D
• E

Q11:

Given that , with , calculate the right Riemann sum for with 5 subintervals of equal width.

Q12:

Given that , with , calculate the midpoint Riemann sum for with 5 subintervals of equal width. Give your answer to three decimal places.

• A60
• B56.877
• C71.001
• D66.082
• E48.954

Q13:

Use a right Riemann sum with 10 subintervals to estimate the area under the curve on the interval . Give your answer to four decimal places.

• A1.3837
• B0.2482
• C0.2767
• D0.2513
• E0.2545

Q14:

Use a midpoint Riemann sum with 6 subintervals to estimate the area under the curve on the interval . Give your answer to two decimal places.

Q15:

Given that , where , calculate the left Riemann sum for with 10 subintervals of equal width. Give your answer to five decimal places.