Skip to content

Course home

Sign up

1.11 H: Integration

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114
Question 26

The current, xxx amps, at time ttt seconds after a switch is closed in an electric circuit is modelled by the differential equation

dxdt=k−2x \frac{dx}{dt} = k - 2x dtdx​=k−2x

where kkk is a constant. Initially, there is no current in the circuit.

a.

Solve the differential equation to show that x=k2(1−e−2t)x = \frac{k}{2}(1 - e^{-2t})x=2k​(1−e−2t).

[4]
b.

In the long term, the current in the circuit approaches 12 amps.

Find the value of kkk.

[2]
c.

Find the time, in seconds, for the current to reach 8 amps, giving your answer to 2 significant figures.

[4]
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