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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.

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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.3: Area And The Definite Integral
Problem 21E
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1 Substitution u =r 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 = / V4x? + 1dx. 1 Substitution u = x² made in the integral L2 1+dx verifies that the length of the second segment is equal to 4х 3 the length of the first segment: L1 / V4x? + 1dx.
Transcribed Image Text:1 Substitution u =r 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 = / V4x? + 1dx. 1 Substitution u = x² made in the integral L2 1+dx verifies that the length of the second segment is equal to 4х 3 the length of the first segment: L1 / V4x? + 1dx.
Consider the curve segments: 1 to x = 3 and 3 1 $1: y = x from x = S2: 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. 9 Substitution u = 3x made in the integral L2 = 1+dx verifies that the length of the second segment is equal to 4x 3 the length of the first segment: L1 = / V4x? + 1dx. 9 Vx made in the integral L2 = 1+dx verifies that the length of the second segment is equal to 4x Substitution u = 3 the length of the first segment: L¡ = V4x + 1dx. Substitution u = Vx made in the integral L2 = 1 + -dx verifies that the length of the second segment is equal to 2x the length of the first segment: L = I V2r + 1dx.
Transcribed Image Text:Consider the curve segments: 1 to x = 3 and 3 1 $1: y = x from x = S2: 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. 9 Substitution u = 3x made in the integral L2 = 1+dx verifies that the length of the second segment is equal to 4x 3 the length of the first segment: L1 = / V4x? + 1dx. 9 Vx made in the integral L2 = 1+dx verifies that the length of the second segment is equal to 4x Substitution u = 3 the length of the first segment: L¡ = V4x + 1dx. Substitution u = Vx made in the integral L2 = 1 + -dx verifies that the length of the second segment is equal to 2x the length of the first segment: L = I V2r + 1dx.
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