I don't get this at all, it looks straightforward but the answer is pretty weird. Can someone explain what swhould I do to solve this
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x = y^(3/2)
dx/dy = (3/2) y^(1/2)
( dx/dy )^2 = (9/4) y
1 + (dx/dy)^2 = 1/4[4 + 9y]
SQRT[1 + (dx/dy)^2 ] = 1/2√(4 + 9y)
arc length, s = 1/2∫√(4 + 9y) dy from 0 to 1
= (1/2)(1/9)(2/3)(4 + 9y)^(3/2)
= (1/27)( 4 + 9y)^(3/2) from [ 0 to 1 ]
= (1/27)[ (4 + 9)^3/2 - (4)^3/2 ]
= 1/27 [46.87 - 8 ]
= 38.87/27
= 1.44
dx/dy = (3/2) y^(1/2)
( dx/dy )^2 = (9/4) y
1 + (dx/dy)^2 = 1/4[4 + 9y]
SQRT[1 + (dx/dy)^2 ] = 1/2√(4 + 9y)
arc length, s = 1/2∫√(4 + 9y) dy from 0 to 1
= (1/2)(1/9)(2/3)(4 + 9y)^(3/2)
= (1/27)( 4 + 9y)^(3/2) from [ 0 to 1 ]
= (1/27)[ (4 + 9)^3/2 - (4)^3/2 ]
= 1/27 [46.87 - 8 ]
= 38.87/27
= 1.44