Integration

• The process of indefinite integration finds a function F whose derivative is a given function (f(V)). If
  
  $$\frac{dp(V)}{dV} = f(V),$$
  
  
  then
  
  $$p(V) = \int f(V) dV + Constant.$$
  
  
  For instance, if
  
  $$f(V) = aV^2 + b \ell n\, V$$
  
  
  then
  
  $$p(V) = \int f(V) dV = a \frac{V^3}{3} + b(V \ell n\, V - V) + Constant$$
  
  
  where the Constant can be any thing which vanishes upon appropriate differentiation.
• The process of definite integration means given a function f(V), and two values of V, finding the area under the graph of f(V) between the aforementioned values of V.
  
  $$\int_a^b f(V) dV = \left [ p(V) \right ]_a^b = p(b) - p(a)$$
  
  
  where p(V) is the indefinite integral of f(V) (the constant of indefinite integration canceled).