Integration
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Question 430
The curve C has the parametric equations
x=6cos2ty=6sint0≤t≤π4 x = 6 \cos 2t \quad y = 6 \sin t \quad 0 \leq t \leq \frac{\pi}{4} x=6cos2ty=6sint0≤t≤4π
The finite region R between the curve C and the x x\,x axis.
a.[2]
The point P is where the curve meets the x x\,x axis. Find the coordinates of P.
b.[5]
Show that the area of R is given by the integral ∫0π4144sin2tcost dt\displaystyle \int_0^{\frac{\pi}{4}} 144 \sin^2 t \cos t\,dt∫04π144sin2tcostdt
c.[5]
Hence find an exact value for the area
Integration Questions
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.