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1.11 H: Integration

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Question 182

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

Given that

  • C C\,C passes through the point P(4,5)P(4, 5)P(4,5)
  • f′(x)=12x2+x−3\displaystyle f'(x) = \frac{12}{x^2} + \sqrt{x} - 3f′(x)=x212​+x​−3
a.

Find the equation of the tangent to C C\,C at PPP. Write 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, in simplest form, f(x)f(x)f(x).

[5]
Markscheme

1.11 H: Integration Questions

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

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, 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). Each one has a worked solution and a mark scheme showing where the marks go.

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