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Question 440

The curve C C\,C has the parametric equations

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

A shaded region R lies between the x-axis and a single arching curve from the origin to a point on the positive x-axis, with coordinate axes shown.

a.

Verify that the area of R R\,R is given by ∫0π212sin⁡tcos⁡2tdt\displaystyle \int_0^{\frac{\pi}{2}} 12 \sin t \cos^2 t dt∫02π​​12sintcos2tdt

[3]
b.

Hence verify, by algebraic integration, that the area of R R\,R is exactly 4

[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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