Skip to content

Course home

Sign up

Integration

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155
Question 151

The profile of a high-precision optical lens is modelled by a curve C C\,C with equation y=f(x)y = f(x)y=f(x) for x>0x > 0x>0.

Given that

  • f′(x)=8x2−(x−4)(2x+5)2xf'(x) = 8x^2 - \dfrac{(x - 4)(2x + 5)}{2\sqrt{x}}f′(x)=8x2−2x​(x−4)(2x+5)​
  • the point P(1,12)P(1, 12)P(1,12) lies on CCC
a.

find the equation of the normal to C C\,C at PPP, giving your answer in the form y=mx+cy = mx + cy=mx+c where m m\,m and c c\,c are constants to be found.

[4]
b.

find f(x)f(x)f(x), giving each term in simplest form.

[5]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank