Numeric vs Symbolic Computation

• One drawback of MATLAB is that, by and large, it can only perform numeric computation, i.e. every MATLAB command causes a number of floating point computations to be made and the resulting number(s) displayed.
• Another area of computation that is beginning to come into its own is symbolic computation, which involves the manipulation of algebraic expressions, and not just numbers.
• The difference between these two types of computation is that, for example, a numeric computation package will only be able to tell you that
  $$\int_0^1 xe^{-x}dx=0.26424\ldots$$
  while a symbolic computation program (i.e., Mathematica, MAPLE) will also tell you that
  $$\int_0^1 xe^{-x}dx=1-2e^{-1}$$

• Solving the integral given above both numerically and symbolically by using MATLAB.