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1.11 H: Integration

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Question 50

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

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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