In this lesson, we will learn how to approximate definite integrals using Simpson’s rule and estimate 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.
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