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1.8 Integration

1.8 Integration

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Question 320
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

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

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