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Question 617

A landscape architect is designing a stylized berm for a public park. The cross-section of the berm's curved face is modeled by the equation

h=4w+1 h = \sqrt{4w + 1} h=4w+1​

where www is the horizontal distance in metres from a reference point and hhh is the height in metres.

The line lll represents a support brace that acts as a normal to the curved face at the point P(6,5)P(6, 5)P(6,5).

a.

Use calculus to show that an equation for the line lll is

5w+2h−40=0 5w + 2h - 40 = 0 5w+2h−40=0
[4]
b.

The region RRR, representing the cross-sectional area of the structure, is bounded by the curved face, the ground line h=0h = 0h=0, and the support brace lll.

Use algebraic integration to find the exact area of RRR.

[6]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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