Skip to content
MathsGenie logo
Open app

Course home

  1. A Level
  3. Maths AQA
  5. Question bank

1 Pure Mathematics

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116
Question 106
a.

Find ∫x2cos⁡3x dx\int x^2 \cos 3x \, dx∫x2cos3xdx

[4]
b.

A spherical weather balloon's volume, VVV m3^33, changes over time ttt seconds during a specific atmospheric test. The rate of change is modeled by the differential equation

dVdt=(tcos⁡1.5t)2V2 \frac{dV}{dt} = \frac{(t \cos 1.5t)^2}{V^2} dtdV​=V2(tcos1.5t)2​

where t≥0t \ge 0t≥0. Solve this differential equation to find VVV in terms of ttt, giving your answer in the form Vn=f(t)V^n = f(t)Vn=f(t) where nnn is an integer.

[5]

1 Pure Mathematics Questions

  1. A Level
  2. /Maths
  3. /1 Pure Mathematics

Question bank