Skip to content

Course home

1.8 Integration

1.8 Integration

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119
Question 73

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+1​

where 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).

a.

Use calculus to show that an equation for the line lll is

5w+2h−40=0 5w + 2h - 40 = 0 5w+2h−40=0
[4]
b.

The 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.

[6]
Markscheme

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

160 exam-style questions on WJEC A Level Maths 1.8 Integration, covering 1.8.1 Integration, 1.8.2 Integration, and 1.8.3 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank