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Lecture

8.1 Arc Length Question #5 (Medium)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
8.1 Challenging Integral Applications Arc Length Question #5 (Medium): Length of a Trajectory Strategy: For functions where evaluating ∫ √ ( ) is challenging, Simpson’s Rule can be used to approximate the length of the curve for the given interval. Sample Question: A trajectory of follows after the given equation. Calculate the total distance traveled before hitting the ground, where is in meters and in seconds. Solution: The interval is not given. So it needs to be determined based on the equation. If it is to count from time 0 until it hits the ground, then ; ; ; √ √ ; √ since t represents time only positive option works. Then total distance travelled is essentially equal to the length of the curve. The derivative of the given √ function is: . Then ∫ √ ( ) ∫ √ ( ) √ √ ∫ ( ) . use substitution where , then . Align the interval as
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