Skip to content

Course home

Sign up

1.11 H: Integration

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118
Question 63

In this question x x\,x and θ \theta\,θ are measured in radians.

a.

Find ∫cos⁡x dx\displaystyle\int \cos x\,dx∫cosxdx.

[1]
b.

You may use the result ddx(tan⁡kx)=ksec⁡2kx\dfrac{d}{dx}(\tan kx) = k\sec^2 kxdxd​(tankx)=ksec2kx. Find ∫2sec⁡24x dx\displaystyle\int 2\sec^2 4x\,dx∫2sec24xdx.

[2]
c.

Hence, using the identity tan⁡2θ≡sec⁡2θ−1\tan^2\theta \equiv \sec^2\theta - 1tan2θ≡sec2θ−1, find ∫tan⁡2θ dθ\displaystyle\int \tan^2\theta\,d\theta∫tan2θdθ.

[2]
Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank