11.1 Integrating Standard Functions
39
0/11
i.

Find

∫(4−3x)25x dx,x>0\int \frac{(4-3x)^2}{5\sqrt{x}} \, dx, \quad x > 0∫5x​(4−3x)2​dx,x>0

giving your answer in simplest form.

[4]
ii.

The rate of change of the depth of water, DDD metres, in a reservoir with respect to time ttt days is modeled by the equation dDdt=t2+at+b\frac{dD}{dt} = t^2 + at + bdtdD​=t2+at+b for 0≤t≤100 \le t \le 100≤t≤10, where aaa and bbb are constants.

  • At the start of a monitoring period (t=0t = 0t=0), the depth is 15 metres.
  • After 3 days, the depth has fallen to 9 metres.
  • On the 3rd day (t=3t = 3t=3), the depth is decreasing at a rate of 2 metres per day.

Determine the expression for DDD in terms of ttt, giving your answer in simplest form.

[7]

11.1 Integrating Standard Functions Questions

Practise Edexcel A Level Maths 11.1 Integrating Standard Functions with exam-style questions for A Level Maths. 81 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

PreviousNext

11.1 Integrating Standard Functions Questions

  1. A Level
  2. /Maths
  3. /11.1 Integrating Standard Functions