![\"\"](\"/userfiles/image/steps_images/step1.JPG\")
Lower sum:
\The sum of the inscribed rectangles is called lower sum.
\Consider function ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=7064e7a30eda712f37b4af317ec3f0b6.png\")
.
Graph the function: ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=7064e7a30eda712f37b4af317ec3f0b6.png\")
.
Observe the graph:
\The function bounded by ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=b2e53498cc30d9d358d484b27fad56ca.png\")
and ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=bea45b6b705e485262881482f9321efe.png\")
.
The inscribed rectangles sum is called lower sum.
\The rectangles in the lower sum do not contain all of the area of the region.
\![\"\"](\"/userfiles/image/steps_images/step2.JPG\")
Upper sum:
\The sum of the circumscribed rectangles is called lower sum.
\Graph the function: .
Observe the graph:
\The function bounded by ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=b2e53498cc30d9d358d484b27fad56ca.png\")
and ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=bea45b6b705e485262881482f9321efe.png\")
.
The circumscribed rectangles sum is called upper sum.
\The rectangles in the upper sum cover more than the area of the region.
\The exact value of the region lies between lower sum and upper sum.
\![\"\"](\"/userfiles/image/steps_images/solution.JPG\")
The rectangles in the lower sum do not contain all of the area of the region and the rectangles in the upper sum cover more than the area of the region.
\The exact value of the region lies between lower sum and upper sum.