Skip to content

Course home

Sign up

1.11.2 Integrating standard functions

EasyMediumHard
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667
Question 56
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

1.11.2 Integrating standard functions Questions

  1. A Level
  2. /Maths
  3. /1.11.2 Integrating standard functions

139 exam-style questions on AQA A Level Maths 1.11.2 Integrating standard functions. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank