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Question 195

The curve C C\,C has the parametric equations

x=3sin⁡ty=6sin⁡2t0≤t≤π2 x = 3 \sin t \quad y = 6 \sin 2t \quad 0 \leq t \leq \frac{\pi}{2} x=3sinty=6sin2t0≤t≤2π​

A Cartesian graph with arrowed x- and y-axes and a shaded region R under a curved line in the first quadrant.

a.

Show that the area of R R\,R is given by ∫0π236sin⁡tcos⁡2tdt\displaystyle \int_0^{\frac{\pi}{2}} 36 \sin t \cos^2 t dt∫02π​​36sintcos2tdt

[3]
b.

Hence show, by algebraic integration, that the area of R R\,R is exactly 12

[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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