Please verify your account before proceeding.
In this lesson, we will learn how to find the arc length of a parametrically defined curve.
Q1:
Calculate the arc length of over the given interval .
Q2:
Find the length of the curve with parametric equations 𝑥 = 3 𝑡 − 3 𝑡 c o s c o s and 𝑦 = 3 𝑡 − 3 𝑡 s i n s i n , where 0 ≤ 𝑡 ≤ 𝜋 .
Q3:
Express the length of the curve with parametric equations 𝑥 = 𝑡 − 2 𝑡 s i n and 𝑦 = 1 − 2 𝑡 c o s , where 0 ≤ 𝑡 ≤ 4 𝜋 , as an integral.
Q4:
Find the length of the curve with parametric equations 𝑥 = 2 𝑡 s i n − 1 and 𝑦 = 1 − 𝑡 l n 2 , where 0 ≤ 𝑡 ≤ 1 2 .
Q5:
Find the length of the curve with parametric equations 𝑥 = 𝑡 𝑡 s i n and 𝑦 = 𝑡 𝑡 c o s , where 0 ≤ 𝑡 ≤ 1 .
Q6:
Express the length of the curve with parametric equations 𝑥 = 𝑡 + 𝑒 − 𝑡 and 𝑦 = 𝑡 − 𝑒 − 𝑡 , where 0 ≤ 𝑡 ≤ 2 , as an integral.
Q7:
Find the length of the curve with parametric equations 𝑥 = 𝑒 − 𝑡 𝑡 and 𝑦 = 4 𝑒 𝑡 2 , where 0 ≤ 𝑡 ≤ 2 .
Q8:
Express the length of the curve with parametric equations 𝑥 = 𝑡 + √ 𝑡 and 𝑦 = 𝑡 − √ 𝑡 , where 0 ≤ 𝑡 ≤ 1 , as an integral.
Q9:
The position of a particle at time 𝑡 is 𝑡 , 𝑡 s i n c o s 2 2 . Find the distance the particle travels between 𝑡 = 0 and 𝑡 = 3 𝜋 .
Q10:
Find the length of the curve with parametric equations 𝑥 = 1 + 3 𝑡 2 and 𝑦 = 4 + 2 𝑡 3 , where 0 ≤ 𝑡 ≤ 1 .
Q11:
Find the length of the curve with parametric equations 𝑥 = 𝑡 2 and 𝑦 = 1 3 𝑡 3 , where 0 ≤ 𝑡 ≤ 1 .
Q12:
Find the length of the astroid with parametric equations 𝑥 = 𝑎 𝜃 c o s 3 and 𝑦 = 𝑎 𝜃 s i n 3 , where 𝑎 > 0 .
Q13:
Find the length of one arch of the cycloid with parametric equations 𝑥 = 𝑟 ( 𝑡 − 𝑡 ) s i n and 𝑦 = 𝑟 ( 1 − 𝑡 ) c o s .
Q14:
Consider the parametric equations 𝑥 = 𝑎 𝜃 c o s and 𝑦 = 𝑎 𝜃 s i n for 0 ≤ 𝜃 ≤ 2 𝜋 .
Express the arclength of this curve as an integral.
Evaluate the integral.
Q15:
Express the length of the curve with parametric equations 𝑥 = 𝑡 − 𝑡 2 and 𝑦 = 𝑡 4 , where 1 ≤ 𝑡 ≤ 4 , as an integral.
Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.
