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Question 654
a.

Prove the identity

sin⁡2x1+tan⁡2x≡2sin⁡xcos⁡3x \frac{\sin 2x}{1 + \tan^2 x} \equiv 2 \sin x \cos^3 x 1+tan2xsin2x​≡2sinxcos3x
[3]
b.

The rate of airflow R R\,R into a mechanical respirator, in litres per second, is modeled by the function

R(t)=10sin⁡6t1+tan⁡23t R(t) = \frac{10 \sin 6t}{1 + \tan^2 3t} R(t)=1+tan23t10sin6t​

where 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.

[4]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

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.

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