Find ∫x2sin2x dx\int x^2 \sin 2x \, dx∫x2sin2xdx
Hence solve the differential equation
dydt=(tsinty)2 \frac{dy}{dt} = \left(\frac{t \sin t}{y}\right)^2 dtdy=(ytsint)2giving your answer in the form yn=f(t)y^n = f(t)yn=f(t) where nnn is an integer.
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.