length of Y=1/3(x^2+2)^3/2 from 0 to 3

Length of Y=1/3(x^2+2)^3/2 from 0 to 3
in Algebra 2 Answers by Level 12 User (101k points)

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8 Answers

By differentiation:
by Level 12 User (101k points)
Y'=x•√x^2+2
by Level 12 User (101k points)
The length L is given by
by Level 12 User (101k points)
(dL/dx)^2=1+(y')^2
by Level 12 User (101k points)
=x^4+2x^2+1
by Level 12 User (101k points)
→(dL/dx)^2=(x^2+1)^2
by Level 12 User (101k points)
→dL/dx=1+x^2
by Level 12 User (101k points)
→L={^3 ° lower(1+x^2)dx=12
by Level 12 User (101k points)

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