The vertical profile of a survey drone is modeled by a curve CCC with equation h=f(t)h = f(t)h=f(t), t>0t > 0t>0, where hhh is the altitude in meters and ttt is the time in seconds. The drone passes through the point P(4,10)P(4, 10)P(4,10).
Given that f′(t)=3t+2−16t2\displaystyle f'(t) = 3\sqrt{t} + 2 - \frac{16}{t^2}f′(t)=3t+2−t216
Find the equation of the normal to CCC at PPP. Write your answer in the form at+bh+c=0at + bh + c = 0at+bh+c=0, where aaa, bbb and ccc are integers to be found.
Find f(t)f(t)f(t).
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.