The arc length of a predator chasing prey (7.4 #65)

 Using the arc length integral we can show that a predator can travel twice the distance in the same amount of time!

Arc Length (7.4 #11)

An exact length of arc can be computed with the arc length formula, together with a bit of algebra, so the integrand is a product of factors where one factor is the derivative of the other so we can use "U-substition"

Exact Arc Length (7.4 # 19)

 

An exact length of arc can be computed with the arc length formula, together with a bit of factoring, recalling a^2+2ab+b^2 = (a + b)^2