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1.8 Integration

1.8 Integration

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Question 101

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

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

160 exam-style questions on WJEC A Level Maths 1.8 Integration, covering 1.8.1 Integration, 1.8.2 Integration, and 1.8.3 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

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