Prove the identity
sin2x1+tan2x≡2sinxcos3x \frac{\sin 2x}{1 + \tan^2 x} \equiv 2 \sin x \cos^3 x 1+tan2xsin2x≡2sinxcos3xThe rate of airflow R R\,R into a mechanical respirator, in litres per second, is modeled by the function
R(t)=10sin6t1+tan23t R(t) = \frac{10 \sin 6t}{1 + \tan^2 3t} R(t)=1+tan23t10sin6twhere t t\,t is the time in seconds. Find an expression for the total volume of air V=∫R(t) dtV = \int R(t) \, dtV=∫R(t)dt.
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.
