Math

 Find an estimate of the area under the graph of

between

= 0

and

= 2

above the

http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7BX%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15

-axis. Use four left endpoint rectangles.

 Find an estimate of the area under the graph of

between

= 0

and

= 2

above the

http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7BX%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15

-axis. Use four right endpoint rectangles.

 Find an estimate of the net area determined by the graph of

between

=-1

and

= 4

. Use four left endpoint rectangles. (A net area is obtained by adding the pieces of the areas above the

-

axis and subtracting the area of the piece below the

http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7BX%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15

-axis.)

 Find an estimate of the area under the graph of

between

= 0

and

= pi

. Use two midpoint rectangles.

 Use elementary geometry to find the area under the graph of

between

=-1

and

= 5

. Sketch a picture.

 The velocity

of an object is sketched below. Estimate the total distance travelled by an object between

= 0

and

= 4

.

 Please share on the forum but do not submit. Good participation points. Design a google spreadsheet that will illustrate Riemann summation. Share the unlisted link on the forum. The entries should be (a) function f(x) [ok to pick a specific function], (b) lower limit a, (c) upper limit b, (d) n - number of rectangles. The result should be three fields: left endpoint, midpoint approximation, right endpoint approximation.