Consider {{MATH_143}}. Approximate the area between the curve {{MATH_144}} and the {{MATH_145}}-axis on the interval {{MATH_146}} using a {{CMD_147}}left-endpoint{{CMD_148}} Riemann sum with {{MATH_149}} rectangles. {{CMD_150}} First note that the width of each rectangle is {{MATH_151}} The grid points define the edges of the rectangle and are seen below: {{CMD_152}} {{ENV_153}} {{CMD_154}} On the other hand, the sample points identify which endpoints we use: {{CMD_155}} {{ENV_156}} {{CMD_157}} It is helpful to collect all of this data into a table: {{MATH_158}} Now we may write a left Riemann sum {{MATH_159}} which evaluates to {{ENV_160}} and we find {{MATH_161}} {{CMD_162}} {{CMD_163}}