Question

arc length of y=(1/4)x^2-(1/2)ln(x) from x=1 to 2

Answer 1

these problems are always cooked up to be doable
did you find \(y'\)?

Answer 2

i think it is
\[y'=\frac{1}{2}x-\frac{1}{2x}\]

Answer 3

then you have to square it

Answer 4

something like
\[\frac{(x^2-1)^2}{4 x^2}\]

Answer 5

then you have to add one to it

Answer 6

and that is where the miracle occurs you get
\[\frac{(x^2+1)^2}{4 x^2}\] which is a perfect square

Answer 7

good thing since now you have to take the square root of it
that gives you
\[\int_1^2\frac{x^2+1}{2x}dx\]

Answer 8

imagine how much work went in to making this problem work out so nicely
i tried it once
took me over half an hour to make one

Answer 9

@satellite73 i did the same way as u said to calculate Arithmetic mean(before asking)