Find the exact length of the curve. Y=y^4/8 + 1/4y^2, 1

ZIHLOLEp3

ZIHLOLEp3

Answered question

2021-11-30

Find the exact length of the curve.
Y=y48+14y2, 1 less than or equal to Y less than or equal 2.

Answer & Explanation

Stephanie Mann

Stephanie Mann

Beginner2021-12-01Added 25 answers

Given:
Y=y48+14y2,1y2
As, the length of the curve, L is given by:
L=ab1+(dydx)2dx
According to the given question, we have:
a=1 , b=2
Since, Y=y48+14y2
Therefore,
dYdy=ddy(y48+14y2)
dYdy=43824y3
dYdy=y32=12y3
Therefore, the length of the given curve is:
L=121+(y3212y3)2dy
L=121+14(y61y3)2dy
L=12(4Y6+(y61)24y6)12dy
L=12(4y6+y122y6+14y6)12dy
L=12(y12+2y6+14y6)12dy

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