How do you find the lengths of the curve y=(x^3)/(12)+1/x for 1 le x le 3?

Custodio88j

Custodio88j

Answered question

2023-02-02

How to find the lengths of the curve y = x 3 12 + 1 x for 1 x 3 ?

Answer & Explanation

incesounckb1

incesounckb1

Beginner2023-02-03Added 6 answers

Step 1
s = 1 3   1 + ( y ) 2     d x
s = 1 3   1 + ( x 2 4 - 1 x 2 ) 2     d x
= 1 3   1 + x 4 16 - 1 2 + 1 x 4     d x
= 1 3   x 4 16 + 1 2 + 1 x 4     d x
= 1 3   ( x 2 4 + 1 x 2 ) 2     d x
= (   x 3 12 - 1 x ) 1 3
Step 2
Hence, = ( 27 12 - 1 3 ) - ( 1 12 - 1 ) = 17 6

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