Worksheet: Numerical Integration: Simpson’s Rule

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

Q3:

Approximate the integral 𝑥𝑥d 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

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

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