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.
480 exam-style questions on AQA A Level Maths 1.11 H: Integration, 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). Each one has a worked solution and a mark scheme showing where the marks go.