Consider the curve segments: 1 $1: y = x² from x =to x = 3 and 3 1 52: y = Vx from x =to x = 9. Set up integrals that give the arc lengths of the curve segments by integrating with respect to x. Demonstrate a substitution that verifies that these two integrals are equal. Substitution u = 3x² made in the integral L2 1 + -dx verifies that the length of the second segment is equal to 4x /- the length of the first segment: L1 = 4x² + ldx. Substitution u = vx made in the integral L2 = 1 + 4x -dx verifies that the length of the second segment is equal to the length of the first segment: L1 = :/ V4x² + 1dx. Substitution u = Vĩ made in the integral L2 = 1+dx verifies that the length of the second segment is equal to 2x 3 the length of the first segment: L1 = /2x + 1dx.

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A: length of arc given below..

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A: Please refer to the image below

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Q: Consider the curve segments: 1 S1: y = x from x =to x = 4 and %3D 2 1 S2: y = Vi from x = - to x =…

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Q: Set up an integral to compute the arc length L of the curve C: r (t) = <글t?, 4t, v26) from the point…

A: Concept of arc length.......

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A: To find the arc length of the given two curves.

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A: It can be found by integrating between limits of t= 0 to 1

Q: Consider the curve segments: 1 $1: y = x from x =to x = 3 and 4 S2: y = Vi from x = to x = 9. 16 Set…

A: Please refer the attached image for complete solution. THANK YOU.

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A: Let's find.

Q: The arc length along the parabola y = x from (1,1) to (2,4) is given by which of the following…

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A: I am going to solve the given problem by using some simple calculus to get the required result.