Skip to content
MathsGenie logo
Quick links
Open app

Course home

  1. A Level
  3. Maths AQA
  5. Question bank

1.11.3 Definite integrals and areas

MediumHard
123456789101112131415161718192021222324
Question 20

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]

1.11.3 Definite integrals and areas Questions

  1. A Level
  2. /Maths
  3. /1.11.3 Definite integrals and areas