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Question 45

Find $dx\int x^2 \cos 4x \, dx$

[4]

A satellite's distance $r$ from a planet is modeled by the differential equation

\frac{dr}{d\theta} = \frac{(\theta \sin 2\theta)^2}{r^2}

where $θ\theta$ is the angular displacement in radians.

Hence solve this differential equation to find an expression for $r^3$ in terms of $θ\theta$ .

[5]

Markscheme

Integration Questions

A Level
Maths
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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Question 45

Find $dx\int x^2 \cos 4x \, dx$

[4]

A satellite's distance $r$ from a planet is modeled by the differential equation

\frac{dr}{d\theta} = \frac{(\theta \sin 2\theta)^2}{r^2}

where $θ\theta$ is the angular displacement in radians.

Hence solve this differential equation to find an expression for $r^3$ in terms of $θ\theta$ .

[5]

Markscheme

Integration Questions

A Level
Maths
Integration