Given that y=tanxy = \tan xy=tanx, use the quotient rule to show that
dydx=sec2x \frac{dy}{dx} = \sec^2 x dxdy=sec2xThe cross-section of a high-precision optical lens is modeled by the region bounded by the curve y=3tan2x+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} 33−3−6πwhich simplifies to
23−π6 2\sqrt{3} - \frac{\pi}{6} 23−6πFully justify your answer.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
