The depth, hhh metres, of an underwater research drone exploring a lake is modelled by a function h(t)h(t)h(t), where t>0t > 0t>0 is the time in seconds after it passes a specific underwater marker.
The vertical acceleration of the drone is given by the equation
h′′(t)=10t3+12t2 h''(t) = \frac{10}{\sqrt{t^3}} + 12t^2 h′′(t)=t310+12t2A point P(1,5)P(1, 5)P(1,5) lies on the depth-time curve.
Given that the rate of change of depth h′(t)=−2h'(t) = -2h′(t)=−2 at point PPP,
find the equation of the normal to the curve at PPP, writing your answer in the form h=mt+ch = mt + ch=mt+c, where mmm and ccc are constants,
determine an expression for h(t)h(t)h(t).
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
