arc length problem?

Question

just wanted to check if my answers right

arc length of y = 3x^2 - 5x + 1 on [-1,4]

i got 40.81

Answer 1

the forumula for arc length is

∫sqrt(1+(y’)^2)

y'=6x-5

y'^2=36x^2-60x+25+1

plugging this into the itegral and evaluating we get

1/144*(72x-60)*sqrt(36x^2-60x+26)+1/12*asinh(6x-5)

evaluating with definite values we get 40.81 ditto.

Answer 2

Yes, you are correct.

The Int(sqrt(36^2-60x+26), x = -1..4) = 40.81083380

Answer 3

depends on type of arc eg polar arc.but you equation displayed does get my tick of approval for basic arc length.