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Lesson: Finding the Arc Length of a Parametrically Defined Curve

In this lesson, we will learn how to find the arc length of a parametrically defined curve.

Worksheet • 15 Questions

Q1:

Calculate the arc length of 𝑓 ( 𝑑 ) = ο€» ο€Ή 𝑑 + 1  𝑑 , ο€Ή 𝑑 + 1  𝑑 , 2 √ 2 𝑑  2 2 c o s s i n over the given interval [ 0 , 1 ] .

  • A 1 0 3
  • B2
  • C 7 2
  • D4
  • E 5 2

Q2:

Find the length of the curve with parametric equations π‘₯ = 3 𝑑 βˆ’ 3 𝑑 c o s c o s and 𝑦 = 3 𝑑 βˆ’ 3 𝑑 s i n s i n , where 0 ≀ 𝑑 ≀ πœ‹ .

Q3:

Express the length of the curve with parametric equations π‘₯ = 𝑑 βˆ’ 2 𝑑 s i n and 𝑦 = 1 βˆ’ 2 𝑑 c o s , where 0 ≀ 𝑑 ≀ 4 πœ‹ , as an integral.

  • A ο„Έ √ 5 βˆ’ 4 𝑑 𝑑 4 πœ‹ 0 c o s d
  • B ο„Έ ( 1 + 2 ( 𝑑 βˆ’ 𝑑 ) ) 𝑑 4 πœ‹ 0 s i n c o s d
  • C ο„Έ √ 5 + 𝑑 βˆ’ 4 𝑑 βˆ’ 4 𝑑 𝑑 𝑑 4 πœ‹ 0 2 c o s s i n d
  • D ο„Έ √ 5 + 4 𝑑 𝑑 4 πœ‹ 0 c o s d
  • E ο„Έ √ 1 + 2 ( 𝑑 βˆ’ 𝑑 ) 𝑑 4 πœ‹ 0 s i n c o s d
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