Integration
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Question 489
The curve C C\,C has the parametric equations
x=2sinty=3sin2t0≤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 graph showing a shaded region R in the first quadrant of a Cartesian coordinate system. The region R is bounded by the x-axis, the y-axis, and a curve that starts at the origin (0,0) and ends at a point on the x-axis. The curve is concave down, reaching a maximum y-value before returning to the x-axis. The x and y axes are labeled with arrows.
a.[3]
Show that the area of R R\,R is given by ∫0π212sintcos2tdt\displaystyle \int_0^{\frac{\pi}{2}} 12 \sin t \cos^2 t dt∫02π12sintcos2tdt
b.[3]
Hence show, by algebraic integration, that the area of R R\,R is exactly 4
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.