Can you explain why the answer for vector parametric equation is incorrect. Also can you explain how to determine limit of integration. Thank you Find the line integral with respect to arc length(5x + 3y)ds, where C is the line segment in the xy-plane with endpoints P = (5, 0) andQ = (0,4).(a) Find a vector parametric equation r(t) for the line segment C so that points P and Q correspond tot = 0 and t = 1, respectively.7(t) = (5 – 5t,4t)(b) Using the parametrization in part (a), the line integral with respect to arc length is(5x + 3y)ds =(25 – 13t) V41 dtwith limits of integration a = 0 and b = 1(c) Evaluate the line integral with respect to arc length in part (b).37 41(5x + 3y)ds =2

Answered: Find the line integral with respect to…

Find the line integral with respect to arc length (5x + 3y)ds, where C is the line segment in the xy-plane with endpoints P = (5, 0) and Q = (0,4).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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Question

Can you explain why the answer for vector parametric equation is incorrect. Also can you explain how to determine limit of integration. Thank you

Find the line integral with respect to arc length
(5x + 3y)ds, where C is the line segment in the xy-plane with endpoints P = (5, 0) and
Q = (0,4).
(a) Find a vector parametric equation r(t) for the line segment C so that points P and Q correspond tot = 0 and t = 1, respectively.
7(t) = (5 – 5t,4t)
(b) Using the parametrization in part (a), the line integral with respect to arc length is
(5x + 3y)ds =
(25 – 13t) V41 dt
with limits of integration a = 0 and b = 1
(c) Evaluate the line integral with respect to arc length in part (b).
37 41
(5x + 3y)ds =
2

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution

Step 1

Given integral
$\int_{C} (5 x + 3 y) d s$
where C is the line segment in x-y plane with the end points P(5,0) and Q(0,4)

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