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Lesson Worksheet: Numerical Integration: Simpson’s Rule Mathematics

In this worksheet, we will practice approximating definite integrals using Simpson’s rule and estimating the error when using it.

Q1:

Use Simpson’s rule with 𝑛=4 to estimate the arc length of the curve 𝑦=𝑒 between 𝑥=1 and 𝑥=3. Give your answer to 5 decimal places.

Q2:

Approximate the integral 𝑥𝑥d using Simpson’s rule with 𝑛=2 subintervals, rounding your answer to one decimal place.

  • A1.4
  • B0.2
  • C1.2
  • D1.9
  • E0.7

Q3:

Approximate the area under the curve 𝑦=𝑓(𝑥) between 𝑥=−1 and 𝑥=5 using Simpson’s rule with 𝑛=6 subintervals.

Q4:

Approximate the area under the curve 𝑦=3 between 𝑥=−2 and 𝑥=2 using Simpson’s rule with 𝑛=4 subintervals, rounding your answer to the nearest whole number.

  • A16
  • B12
  • C24
  • D8
  • E6

Q5:

Approximate the area under the given curve between 𝑥=−2 and 𝑥=2 using Simpson’s rule with 𝑛=4 subintervals.

  • A1663
  • B2209
  • C11027
  • D22027
  • E1109

Q6:

Use Simpson’s rule with 4 equal subintervals to approximate the integration 𝐼=𝑥𝑥arccosd to four decimal places.

Q7:

Use Simpson’s rule with 4 equal subintervals to approximate the integration 𝐼=2𝑥𝑥cosd. Approximate your answer to four decimal places.

Q8:

Use Simpson’s rule with the subinterval 𝑛=4 to approximate the integration 𝐼=𝑒𝑥d. Approximate your answer to four decimal places.

Q9:

Use Simpson’s rule with 𝑛=4 subinterval to approximate the integration 𝐼=11+𝑥𝑥d. Approximate your answer to four decimal places.

Find the exact value of the absolute error. Approximate your answer to four decimal places.

Q10:

Use Simpson’s rule with 𝑛=4 subintervals to approximate the integration 𝐼=1𝑥𝑥d. Approximate your answer to four decimal places.

The estimated error is calculated using the following formula: 𝐸=(𝑏−𝑎)180×𝑛𝑓(𝜁),𝑎≤𝜁≤𝑏.()where:

Find the absolute difference between the exact error and the bound of the estimated error. Give your answer to four decimal places.

This lesson includes 54 additional question variations for subscribers.

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