What is the distance, along the graph, of x squared (between 0 and 1, say)?

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What is the distance, along the graph, of x squared (between 0 and 1, say)?

2007-10-12 00:00:32 · 2 answers · asked by pobafett 2 in Science & Mathematics ➔ Mathematics

2 answers

the length of the curve is given by the formula

int of √{1+(dy/dx)^2} between limits

you then have to find a method to do the integration - still thinking about it!!!

2007-10-12 00:30:09 · answer #1 · answered by Anonymous · 0⤊ 0⤋

L= Int(0,1) sqrt(1+4x^2)dx=2Int (0,1)sqrt(1/4+x^2)dz =
2[x/2*sqrt(1/4+x^2)+1/8*ln(x+sqrt(1/4+x^2)] (0,1)
=2(1/2*sqrt(5/4)+1/8ln(1+sqrt5/4)+1/8ln2=
sqrt(5/4)+1/4* ln(2+2sqrt(5/4))
I saw they cut the integral.
Int sqrt(1/4+x^2)= x/2*sqrt(1/4+x^2)+1/8(ln(x+sqrt(1/4+x^2))

2007-10-12 09:13:23 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋