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3.6 Integration (A-level only)

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Question 81

The profile of a precision parabolic reflector is modeled by the curve with equation

y=3x2+512x3−100,x>0 y = 3x^2 + \frac{512}{\sqrt{x^3}} - 100, \quad x > 0 y=3x2+x3​512​−100,x>0

where xxx and yyy are measured in decimetres. The point PPP is the only stationary point on the curve.

a.

Use calculus to show that the xxx-coordinate of PPP is 4.

[3]
b.

A horizontal support strut, lll, is positioned such that it passes through point PPP and is parallel to the xxx-axis. The region RRR is bounded by the reflector's profile, the strut lll, and the vertical casing at x=1x = 1x=1.

Use algebraic integration to find the exact area of RRR.

[6]
Markscheme

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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