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.
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.