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Worksheet: Area Enclosed by a Parametric Curve

Q1:

Consider the curve defined by the parametric equations π‘₯ = 𝑝 3 and 𝑦 = 4 βˆ’ 𝑝 2 .

Find the area under the curve where 0 ≀ 𝑝 ≀ 1 .

Find the area under the curve where 0 ≀ 𝑝 ≀ 2 .

Q2:

Consider the curve defined by the parametric equations π‘₯ = 2 𝑑 c o s and 𝑦 = 3 𝑑 s i n .

Find ο„Έ βˆ’ 6 𝑑 𝑑 s i n d 2 .

  • A βˆ’ 3 𝑑 βˆ’ 3 2 2 𝑑 + 𝑐 s i n
  • B 3 𝑑 + 3 2 2 𝑑 + 𝑐 s i n
  • C βˆ’ 3 𝑑 + 1 2 2 𝑑 + 𝑐 s i n
  • D βˆ’ 3 𝑑 + 3 2 2 𝑑 + 𝑐 s i n
  • E βˆ’ 6 𝑑 + 3 2 2 𝑑 + 𝑐 s i n

Find the area under the curve when 0 ≀ 𝑑 ≀ πœ‹ .

  • A 3 πœ‹
  • B πœ‹ 3
  • C 2 πœ‹
  • D πœ‹
  • E 6 πœ‹

Now, by taking 0 ≀ 𝑑 ≀ 2 πœ‹ , find the total area inside the curve.

  • A πœ‹
  • B 3 πœ‹
  • C 6 πœ‹
  • D πœ‹ 3
  • E 2 πœ‹