Original
The definite integral computes the net area (sum of signed areas) between {{MATH_138}} and the {{MATH_139}}-axis on the
interval {{MATH_140}}.
{{COMMENT_141}}
{{COMMENT_142}}
{{COMMENT_143}}
{{COMMENT_144}}
{{COMMENT_145}}
{{COMMENT_146}}
{{CMD_147}}
Consider the graph of a function {{MATH_148}} on the interval {{MATH_149}}.
{{CMD_150}}
{{ENV_151}}
{{CMD_152}}
Compute the definite integral
{{MATH_153}}
{{CMD_154}}
The net area in the figure above is given by
{{MATH_155}}
The areas {{MATH_156}} and {{MATH_157}} are easily computed, since both are the areas of triangles. Therefore,
{{MATH_158}}
{{CMD_159}}
{{CMD_160}}
There is more to this example, than just a value of the integral.