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Question 142

The profile of a specialized aerodynamic sail is modeled by a curve with parametric equations

x=36−6t,y=t336+6t,0≤t≤6 x = \sqrt{36-6t}, \quad y = \frac{t^3}{\sqrt{36+6t}}, \quad 0 \le t \le 6 x=36−6t​,y=36+6t​t3​,0≤t≤6

The curve intersects the yyy-axis at the point where t=6t=6t=6 and the xxx-axis at the point where t=0t=0t=0. The region RRR is bounded by the curve and the positive xxx and yyy axes.

a.

Show that the area of RRR is given by

K∫06t31296−36t2 dt K \int_{0}^{6} \frac{t^3}{\sqrt{1296-36t^2}} \, dt K∫06​1296−36t2​t3​dt

where KKK is a constant to be found.

[4]
b.

Using the substitution u=1296−36t2u = 1296 - 36t^2u=1296−36t2, or otherwise, find the exact area of RRR.

[7]
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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