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1.9.24 Integrate e^kx, 1/x, sin kx, cos kx (A-level only)

1.9.24 Integrate e^kx, 1/x, sin kx, cos kx (A-level only)

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Question 26
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

1.9.24 Integrate e^kx, 1/x, sin kx, cos kx (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.9.24 Integrate e^kx, 1/x, sin kx, cos kx (A-level only)

31 exam-style questions on OCR (MEI) A Level Maths 1.9.24 Integrate e^kx, 1/x, sin kx, cos kx (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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