Skip to content

Course home

Sign up

3.7.1 Integration (A-level only)

EasyMediumHard
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647
Question 47

A scientist models the rate of temperature change, dTdt\frac{dT}{dt}dtdT​, of a new alloy using the equation

dTdt=9t3t2+k \frac{dT}{dt} = \frac{9t}{3t^2 + k} dtdT​=3t2+k9t​

where t≥0t \ge 0t≥0 is the time in seconds and kkk is a positive constant.

a.

Find

∫9t3t2+k dt \int \frac{9t}{3t^2 + k} \, dt ∫3t2+k9t​dt
[2]
b.

Given that the change in temperature between t=0t = 0t=0 and t=2t = 2t=2 is exactly ln⁡125\ln 125ln125 degrees, determine the value of kkk.

[4]
Markscheme

3.7.1 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.7.1 Integration (A-level only)

67 exam-style questions on WJEC A Level Maths 3.7.1 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank