The rate of change of the altitude of a meteorological probe, HHH, in meters per second with respect to time ttt, is modeled by the function
v(t)=6t2−94t3,t>0 v(t) = \frac{6t^2 - 9}{4\sqrt[3]{t}}, \quad t > 0 v(t)=43t6t2−9,t>0Determine the general expression for the altitude H(t)H(t)H(t) of the probe, giving your answer in its simplest form.
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.