Changes

:::<math>\int_a^b f(x)\,dx</math>

:::<math>\int_a^b f(x)\,dx</math>

The "obvious" way to evaluate such an integral is to divide the domain of the function into many small intervals (this division is called a ''mesh'') and to visualize the area under the function as being the sum of the areas of the rectangular strips created by the mesh.  The height of each strip is hard to measure accurately, because the function value is typically not constant across the interval.  What is done is to choose some value that approximately represents the the function value on the interval, multiply by the interval width (strip width) and take that as the area of the strip.  The representation of the function value is generally taken as

The "obvious" way to evaluate such an integral is to divide the domain of the function into many small intervals (this division is called a ''mesh'') and to visualize the area under the function as being the sum of the areas of the rectangular strips created by the mesh.  The height of each strip is hard to measure accurately, because the function value is typically not constant across the interval.  What is done is to choose some value that approximately represents the function value on the interval, multiply by the interval width (strip width) and take that as the area of the strip.  The representation of the function value is generally taken as

*The function value at the left edge of the interval.

*The function value at the left edge of the interval.

*The function value at the right edge of the interval.

*The function value at the right edge of the interval.