IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

jatinroxx

Find the length of a curve y = f(x) in the interval a to b

The curve is continuous and differentiable in the given interval

Question not for astronauts nd punters 'coz they have already bin told the answers.

jus_look

is it:

the whole integral of { [f(b)-f(a)]/(b-a)dx}

jatinroxx

Dude, this isnt as easy as just stating a theorem.

jus_look

k..nudge me when u wanna tell the answer...
thnx

ashwin123

consider a curve y=f(x),

now take a section

s of the curve.

draw

x and

y respectively.

you can then get (

s)^2=(

x)^2+(

y)^2

Divide by (

x)^2 and take limits you get

(ds/dx)^2=1+(dy/dx)^2

therfore we get

ds/dx=sqrt(1+(dy/dx)^2)

ds=sqrt(1+(dy/dx)^2)dx

ds=_a]^{[b ]} sqrt(1+(dy/dx)^2)dx

this is your ans

ashwin123

pls rate me yaar.no one does

ramyadiamond

It would be given by l=_{[ a]}^{[ b]}

1+y^'2 dx

where y^'is the derivative of the function.