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Question 426

The curve C C\,C has the parametric equations

x=5sin⁡ty=6sin⁡2t0≤t≤π2 x = 5 \sin t \quad y = 6 \sin 2t \quad 0 \leq t \leq \frac{\pi}{2} x=5sinty=6sin2t0≤t≤2π​

Figure 1 shows a shaded region R bounded by a first-quadrant curve and the coordinate axes.

a.

Show that the area of R R\,R is given by ∫0π260sin⁡tcos⁡2t dt\displaystyle \int_0^{\frac{\pi}{2}} 60 \sin t \cos^2 t\,dt∫02π​​60sintcos2tdt

[3]
b.

Hence show, by algebraic integration, that the area of R R\,R is exactly 20

[3]
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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