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 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.
