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Question 455
a.

Given that y=tan⁡xy = \tan xy=tanx, use the quotient rule to show that

dydx=sec⁡2x \frac{dy}{dx} = \sec^2 x dxdy​=sec2x
[3]
b.

The cross-section of a high-precision optical lens is modeled by the region bounded by the curve y=3tan⁡2x+2y = 3\tan^2 x + 2y=3tan2x+2, the xxx-axis, and the vertical boundaries x=π6x = \frac{\pi}{6}x=6π​ and x=π3x = \frac{\pi}{3}x=3π​.

Show that the area of this cross-section is

33−3−π6 3\sqrt{3} - \sqrt{3} - \frac{\pi}{6} 33​−3​−6π​

which simplifies to

23−π6 2\sqrt{3} - \frac{\pi}{6} 23​−6π​

Fully justify your answer.

[5]
Markscheme

Integration Questions

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

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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