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1.11 H: Integration

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Question 235
a.

Find the equation of the tangent to the curve with equation

y=16x3−9x12 y = \frac{1}{6}x^3 - 9x^\frac{1}{2} y=61​x3−9x21​

at the point P(9,94.5)P(9, 94.5)P(9,94.5).

Give your answer in the form ax+by+c=0ax + by + c = 0ax+by+c=0, where aaa, bbb and ccc are integers.

[5]
b.

The curve with equation y=f(x)y = f(x)y=f(x) also passes through the point P(9,94.5)P(9, 94.5)P(9,94.5). Given that

f′(x)=16x3−9x12 f'(x) = \frac{1}{6}x^3 - 9x^\frac{1}{2} f′(x)=61​x3−9x21​

find f(x)f(x)f(x), giving the coefficients in simplest form.

[4]
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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