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+x3512−100,x>0where xxx and yyy are measured in decimetres. The point PPP is the only stationary point on the curve.
Use calculus to show that the xxx-coordinate of PPP is 4.
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.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
