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Worksheet: Area between Curves and the x-Axis

Q1:

Determine the area of the plane region bounded by the curve 𝑦 = 8 π‘₯ 4 and the lines π‘₯ = 1 , π‘₯ = 8 , and 𝑦 = 0 rounded to the nearest hundredth.

Q2:

A glassed, arched entry to a hotel follows the curve 𝑦 = βˆ’ 1 2 ( π‘₯ βˆ’ 9 ) ( π‘₯ βˆ’ 3 ) , where 𝑦 is the vertical height of the arch at a distance of π‘₯ metres from the floor. If glass costs 1 190 LE per square metre, calculate the cost of the entrance.

Q3:

Determine the area of the plane region bounded by the curve 𝑦 = βˆ’ 3 π‘₯ βˆ’ 6 π‘₯ + 9 2 and the π‘₯ -axis rounded to the nearest hundredth.

Q4:

The curve shown is 𝑦 = 1 π‘₯ . What is the area of the shaded region? Give an exact answer.

  • A1.09861228866811
  • B βˆ’ ( 3 ) l n
  • C βˆ’ 1 . 0 9 8 6 1 2 2 8 8 6 6 8 1 1
  • D l n ( 3 )
  • E βˆ’ ( 4 ) l n

Q5:

The curve shown is 𝑦 = 1 π‘₯ . What is the area of the shaded region? Give an exact answer.

  • A1.09861228866811
  • B βˆ’ ( 3 ) l n
  • C βˆ’ 1 . 0 9 8 6 1 2 2 8 8 6 6 8 1 1
  • D l n ( 3 )
  • E l n ( 4 )

Q6:

The figure shows the graph of 𝑓 ( π‘₯ ) = 1 4 ( π‘₯ βˆ’ 2 ) ( π‘₯ + 1 ) 2 .

Calculate the area of the shaded region, giving your answer as a fraction.

  • A 5 1 6
  • B 2 7 4
  • C 5 4
  • D 2 7 1 6
  • E 1 3 1 6

Q7:

The curve shown is 𝑦 = 1 π‘₯ . What is the area of the shaded region? Give an exact answer.

  • A0.4054651081
  • B1.09861228866811
  • C1.584962501
  • D l n ( 3 )
  • E l n ( 2 )

Q8:

Let 𝑓 ( π‘₯ ) = 2 π‘₯ + 3 2 . Determine the area bounded by the curve 𝑦 = 𝑓 ( π‘₯ ) , the π‘₯ -axis, and the two lines π‘₯ = βˆ’ 1 and π‘₯ = 5 .

  • A 9 0 square units
  • B 2 7 0 square units
  • C 2 8 4 3 square units
  • D 1 0 2 square units