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Question 355

The curve C has the parametric equations

x=3cos⁡2ty=3sin⁡t0≤t≤π4 x = 3 \cos 2t \quad y = 3 \sin t \quad 0 \leq t \leq \frac{\pi}{4} x=3cos2ty=3sint0≤t≤4π​

A first-quadrant graph of curve C with point P on the x-axis and region R between the curve and the x-axis.

The finite region R between the curve C and the x x\,x axis.

a.

The point P is where the curve meets the x x\,x axis. Find the coordinates of P.

[2]
b.

Show that the area of R is given by the integral ∫0π436sin⁡2tcos⁡tdt\displaystyle \int_0^{\frac{\pi}{4}} 36 \sin^2 t \cos t dt∫04π​​36sin2tcostdt

[5]
c.

Hence find an exact value for the area

[5]
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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