text: Math Application integral calculus Calculating areas with integrals
  
  # Area under a curve
  
  The area between a curve and the x-axis can be calculated with the definite integral.
  
  Here is a short overview. You can find more information about calculating areas with integrals in the corresponding article.
  
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  ### Remember
  
  For the definite integral, the partitions above the x-axis are positive and those below, negative.
  
  ## Functions without change of sign
  
  The area under a function $f(x)$ without change of sign over $[a; b]$ corresponds to the absolute value of the definite integral.
  
  $A=|\int_a^b f(x)\,\mathrm{d}x|$
  
  ## Functions with change of sign
  
  The area is partly above and partly below the x-axis. The divided areas must therefore be calculated and added separately.
  
  $A=A_1+A_2$
  
  ## Area between curves
  
  The enclosed area in the interval $[a; b]$ is calculated by the formula:
  
  $A=|\int_a^b (f(x)-g(x))\,\mathrm{d}x|$