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1.8 Integration

1.8 Integration

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Question 280
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

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

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