Applications of the Integral
Problems
Problem : Suppose a dog named Tika is chasing a duck in a straight line. If the duck's speed is given by d'(t) = 5 feet per second and Tika's speed by T'(t) = 2t feet per second, how far has Tika traveled when her speed is equal to the duck's speed? If the duck gets a 100 foot head start, how far has Tika traveled when she catches the duck?
Figure %: The Dog Tika Chasing a Duck
2tdt = (t
2|0
5/2) = 
)/2
