Lesson: Arc Length of a Curve y = ƒ(x)

In this lesson, we will learn how to set up the integral which gives the arc length of the smooth curve defined as y=f(x) between two points.

Worksheet: Arc Length of a Curve y = ƒ(x) • 6 Questions

Q1:

Write the integral required to calculate the length of the sine curve between and . Do not evaluate it.

Q2:

Work out the length of the arc between and . Give your answer as a fraction.

Q3:

Using a trigonometric substitution, determine the arc length of the curve between and .

Q4:

Calculate the arc length of the curve between and , giving your answer to 5 decimal places.

Q5:

Find the function which gives the length of the arc from to .

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