Integration by Substitution. The rate of growth of Grass carp, one of the most common type of fish, was modelled by the equation f(t ) = - 2x + 4 x2 + 4x + 3 where t is measured in years and f(t) in kilograms per year. Consider the integral 2x + 4 - dx x2 + 4x + 3 After substitution into u, the new integral can be written A du (a) The value of A is 0 4 Ox+2 O 2x O X O 2x + 2 0 2 (b) The upper limit of integration b is 0 4 O 48 O -24 O -8 O 24 O 16 O 8