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1.11 H: Integration

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Question 273

The curve C C\,C has equation y=f(x)y = f(x)y=f(x) where x>0x > 0x>0.

Given that

  • f′(x)=10x−(x+1)(2x−3)2xf'(x) = 10x - \dfrac{(x + 1)(2x - 3)}{2\sqrt{x}}f′(x)=10x−2x​(x+1)(2x−3)​
  • the point P(1,4)P(1, 4)P(1,4) 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.

[7]

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions 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), matched to the AQA A Level Maths (7357) 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.

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