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).
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.