(0,0) , (8,15) Find the distance between the two points using integration.

 Given the equation of a line y = mx + b,
=> slope = dy/dx = m . Thus, the distance is:
L = int_a^b sqrt(1+(dy/dx)^2) dx  , a<=x<=b 
 
we know the two points (x_1,y_1)=(0,0)
(x_2,y_2)=(8,15)
m = (y_2- y_1)/(x_2-x_1) = (15-0)/(8-0) = 15/8
so now the length is L = int_0^8 sqrt(1+(15/8)^2) dx
 = int_0^8 sqrt(1+(225/64)) dx
 = int_0^8 sqrt((64+225)/64)) dx
= int_0^8 sqrt((289)/64)) dx
= int_0^8 (17/8) dx
= (17/8) int_0^8 1 dx  
= (17/8) |_0^8 x 
= (17/8 )[8-0]
= 17
so the distance between the two points = 17