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Worksheet: Finding the Total Area Bounded by Alternating Functions

Q1:

The curve in the figure is 𝑦 = 1 5 ο€Ή π‘₯ βˆ’ 3 π‘₯ + 4  3 2 .

What is the area of the shaded region? Give your answer exactly as a fraction.

  • A 2 5 7 3 2
  • B 2 1 2 0
  • C 2 1 4
  • D 2 5 7 1 6 0
  • E 5 5 3 3 2 0

Q2:

The curves shown are and . What is the area of the shaded region? Give an exact answer.

  • A
  • B
  • C
  • D
  • E

Q3:

Find the area of the region bounded by 𝑦 = 3 π‘₯ βˆ’ 4 c o s and 𝑦 = βˆ’ 5 π‘₯ c o s , where 0 ≀ π‘₯ ≀ 2 πœ‹ .

  • A βˆ’ 2 √ 3 + 1 6 πœ‹ 3
  • B 2 √ 3 + 1 6 πœ‹ 3
  • C 1 6 πœ‹ 3
  • D 8 √ 3 + 1 6 πœ‹ 3
  • E 3 √ 3 + 1 6 πœ‹ 3

Q4:

Find the area of the region bounded by 𝑦 = π‘₯ βˆ’ 3 c o s and 𝑦 = βˆ’ 5 π‘₯ c o s , where 0 ≀ π‘₯ ≀ 2 πœ‹ .

  • A βˆ’ 4 √ 3 + 4 πœ‹
  • B 4 √ 3 + 4 πœ‹
  • C 4 πœ‹
  • D 6 √ 3 + 4 πœ‹
  • E √ 3 + 4 πœ‹

Q5:

Find the area of the region bounded by 𝑦 = π‘₯ c o s and 𝑦 = βˆ’ 3 π‘₯ + 2 c o s , where 0 ≀ π‘₯ ≀ πœ‹ .

  • A βˆ’ 1 + 2 πœ‹ 3 + 3 √ 3
  • B βˆ’ 3 + √ 3 + 2 πœ‹ 3
  • C βˆ’ 2 πœ‹ 3 + 4
  • D 2 πœ‹ 3 + 4 √ 3
  • E 4 + 4 πœ‹ 3

Q6:

Determine, to the nearest thousandth, the area of the region bounded by the graph of the function 𝑓 ∢ 𝑓 ( π‘₯ ) = ( π‘₯ βˆ’ 8 ) ( π‘₯ βˆ’ 3 ) ( π‘₯ βˆ’ 2 ) , where 𝑓 ( π‘₯ ) β‰₯ 0 , and the lines π‘₯ = 9 and 𝑦 = 0 .