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Applications of integral calculus — Question 296

Original QCE Vault practice · 5 marks

Q296 · Practice questionTechnology-activeSimple familiar5 marks

QUESTION 296 (5 marks)

A channel has the depths in the supplied table, measured at equally spaced positions across its 4 m width. The water has uniform downstream speed 0.75 m/s. The flow rate equals cross-sectional area times downstream speed.
Question 149 stimulus; see the question for exact data and required construction.
a)
Use Simpson's rule with four strips to estimate the cross-sectional area. Show the substituted ordinates.
[3 marks]
b)
A worker estimates the flow rate as 2.5 m3^3/s. Evaluate the estimate using your result.
[1 mark]
c)
State one way to improve the area approximation using Simpson's rule.
[1 mark]
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