Find ∫x2cos4x dx\int x^2 \cos 4x \, dx∫x2cos4xdx
A satellite's distance rrr from a planet is modeled by the differential equation
drdθ=(θsin2θ)2r2 \frac{dr}{d\theta} = \frac{(\theta \sin 2\theta)^2}{r^2} dθdr=r2(θsin2θ)2where θ\thetaθ is the angular displacement in radians.
Hence solve this differential equation to find an expression for r3r^3r3 in terms of θ\thetaθ.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
