Integration
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Question 390
The curve C has the parametric equations
x=3cos2ty=3sint0≤t≤π4 x = 3 \cos 2t \quad y = 3 \sin t \quad 0 \leq t \leq \frac{\pi}{4} x=3cos2ty=3sint0≤t≤4π
Graph of curve C in the first quadrant. The curve starts at (3,0)(3, 0)(3,0) and ends at (0,3)(0, 3)(0,3). It is a hump-shaped curve opening downwards, with its peak at (0,3)(0, 3)(0,3). The area under the curve between the xxx-axis and the curve is shaded with diagonal lines.
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.[1]
Find dxdt\displaystyle \frac{dx}{dt}dtdx.
c.[4]
Show that the area of R is given by the integral ∫0π436sin2tcost dt\displaystyle \int_0^{\frac{\pi}{4}} 36 \sin^2 t \cos t\,dt∫04π36sin2tcostdt
d.[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.