Example 7.   Let  [Graphics:Images/RiemannSumMod_gr_119.gif]  over  [Graphics:Images/RiemannSumMod_gr_120.gif].  
7 (a) Find the formula for the right Riemann sum using n subintervals.
7 (b) Find the limit of the right Riemann sum in part (a).

Solution 7 (a).

(a) Find the formula for the right Riemann sum using n subintervals.

[Graphics:../Images/RiemannSumMod_gr_121.gif]


[Graphics:../Images/RiemannSumMod_gr_122.gif]
[Graphics:../Images/RiemannSumMod_gr_123.gif]
[Graphics:../Images/RiemannSumMod_gr_124.gif]

[Graphics:../Images/RiemannSumMod_gr_125.gif]

[Graphics:../Images/RiemannSumMod_gr_126.gif]

[Graphics:../Images/RiemannSumMod_gr_127.gif]
[Graphics:../Images/RiemannSumMod_gr_128.gif]
[Graphics:../Images/RiemannSumMod_gr_129.gif]
[Graphics:../Images/RiemannSumMod_gr_130.gif]
[Graphics:../Images/RiemannSumMod_gr_131.gif]

[Graphics:../Images/RiemannSumMod_gr_132.gif]

 

Solution 7 (b).

(b) Find the limit of the right Riemann sum in part (a).

[Graphics:../Images/RiemannSumMod_gr_133.gif]

[Graphics:../Images/RiemannSumMod_gr_134.gif]

[Graphics:../Images/RiemannSumMod_gr_135.gif]
[Graphics:../Images/RiemannSumMod_gr_136.gif]

[Graphics:../Images/RiemannSumMod_gr_137.gif]

[Graphics:../Images/RiemannSumMod_gr_138.gif]

[Graphics:../Images/RiemannSumMod_gr_139.gif]

[Graphics:../Images/RiemannSumMod_gr_140.gif]

[Graphics:../Images/RiemannSumMod_gr_141.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004