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1.8 Integration

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Question 87

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

Given that

$8x^2 - \dfrac{(x - 4)(2x + 5)}{2\sqrt{x}}$
the point $P (1, 12)$ lies on $C$

a.

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

[4]

b.

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

[5]

Markscheme

1.8 Integration Questions

A Level
Maths
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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