Find the exact length of the curve.MSKx=1/3, (y)^{1/2}(y-3),1\leq y\leq9

ruigE

ruigE

Answered question

2021-09-25

Find the exact length of the curve.

x=13,(y)12(y3),1y9

Answer & Explanation

irwchh

irwchh

Skilled2021-09-26Added 102 answers

Length of the curve y=f(x) between x=a and x=b is
L=ab((dxdy+1)2)
x=13y(y3) fo 1y9
Differentiate to get
dxdy=13×12y×(y3)+13×y
dxdy=13×12y×(y3)+13×y×2y2y
dxdy=13(y3+2y2y)
dxdy=13(3y32y)
dxdy=(y12y)
Length of the curve is
L=19(dxdy)2+1dy
=19(y1)24y+1dy
=19(y1)2+4y4ydy
=19(y2+2y+1)4ydy
=19(y+1)24ydy

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