Find ∫x2cos3x dx\int x^2 \cos 3x \, dx∫x2cos3xdx
A spherical weather balloon's volume, VVV m3^33, changes over time ttt seconds during a specific atmospheric test. The rate of change is modeled by the differential equation
dVdt=(tcos1.5t)2V2 \frac{dV}{dt} = \frac{(t \cos 1.5t)^2}{V^2} dtdV=V2(tcos1.5t)2where t≥0t \ge 0t≥0. Solve this differential equation to find VVV in terms of ttt, giving your answer in the form Vn=f(t)V^n = f(t)Vn=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.