Question

integral for calculating the length of arc of parabola y^2=4x, cut off by the line 3y=8 is​

Answer 1

Answer:

The formula is simple enough (see Calculus II - Arc Length).

So is the derivative.

But life gets positively nasty when we calculate the integral. I used wolfram-alpha.

The two functions intersect at the origin and where [math]x=\frac{9a}{16}[/math]. Again, wolfram-alpha obliges with the definite integral when I enter,

integrate sqrt(1+(a/sqrt(ax))^2) from 0 to 9a/16