The profile of a specialized parabolic drainage channel is modeled by the curve with equation
h(x)=2x2+256x−100,x>0 h(x) = 2x^2 + \frac{256}{\sqrt{x}} - 100, \quad x > 0 h(x)=2x2+x256−100,x>0where hhh is the depth in millimeters and xxx is the horizontal distance from the left edge of the sensor assembly. The point PPP is the minimum point on the curve.
Use calculus to show that the xxx-coordinate of PPP is 4.
A horizontal laser beam, represented by the line lll, passes through point PPP and is parallel to the xxx-axis. A shaded region RRR is bounded by the curve, the laser beam lll, and the vertical line x=1x = 1x=1.
Use algebraic integration to find the exact cross-sectional area of the region RRR.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) 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.
