Calculus Test 1 Spring 2016 x M MathwaylMath Problem s x c calculus questionIChe

Question

Calculus Test 1 Spring 2016 x M MathwaylMath Problem s x c calculus questionIChegg.... x G integral symbol Google s x a712 unread fonklaw Y... x 3 www.webassign.net/web/student/Assignment-Responses/submit?dep-13238844 15. -6.25 points LarCalc10 7.4.007 Find the arc length of the graph of the function over the indicated interval. (Round your answer to three decimal places.) y 3x2/3, 27, 1251 Home My Assignments Extension Requesf WebAasign8 4.0 e 1997-2016 Advanced Instructional Systems. Inc All rights reserved. Firefox automatically sends some data to Mozilla so that we can improve your experience. a search My Notes o Ask Your Teacher My Notes Ask Your Teacher My Notes Ask Your Teacher Choose What Share x 2/29/2016

Explanation / Answer

Calculate the arc length of y = (2/3)x^(3/2) over the interval [27,125]. The arc length, L, is given by:

L = [1 + (dy/dx)²] dx

Given y = (2/3)x^(3/2), the derivative, dy/dx = x, therefore:

L = [1 + (x)²] dx = [27,125] (1 + x)] dx

Integrating:

L = (2/3)(1 + x)^(3/2) evaluated over the interval [27,125]

Evaluating:

L = (2/3)[(1 + 125)^(3/2) - (1 + 27)^(3/2)] = (2/3)[1414.34 - 148.162] = 844.118 units

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