A landscape architect is designing a stylized berm for a public park. The cross-section of the berm's curved face is modeled by the equation
h=4w+1 h = \sqrt{4w + 1} h=4w+1where www is the horizontal distance in metres from a reference point and hhh is the height in metres.
The line lll represents a support brace that acts as a normal to the curved face at the point P(6,5)P(6, 5)P(6,5).
Use calculus to show that an equation for the line lll is
5w+2h−40=0 5w + 2h - 40 = 0 5w+2h−40=0The region RRR, representing the cross-sectional area of the structure, is bounded by the curved face, the ground line h=0h = 0h=0, and the support brace lll.
Use algebraic integration to find the exact area of 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.
