Consider the curve segments: 1 to x = 2 and 3 1 to x = 4. S1: y = x from x = S2: y = Vx from x = 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. Vx made in the integral L2 = 1 1+dx verifies that the length of the second segment is equal to 2x Substitution u = the length of the first segment: L1 = V2x + 1dx. 4 made in the integral L2 1 + -dx verifies that the length of the second segment is equal to 4x Substitution u = the length of the first segment: L1 = V4x? + ldx. Vx made in the integral L2 = 1 -dx verifies that the length of the second segment is equal to 4x Substitution u = 1 + the length of the first segment: L1 = V4x + 1dx. 4 2x made in the integral L2 = 1+dx verifies that the length of the second segment is equal to 4х Substitution u = the length of the first segment: L1 = / V4x + 1dx. 4 Substitution u = x 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 = V4x? + ldx.

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