Definite Integrals
Example 1
Let R be the region between the graph y = f ( x ) = x^{2} + 1 and the xaxis on the interval [0,4]: Use a lefthand sum with two subintervals to approximate the area of R. 
Example 2
Let R be the region between the graph y = f ( x ) = x^{2} + 1 and the xaxis on the interval [0,4]. Use a LeftHand Sum with 4 subintervals to estimate the area of R. 
Example 3
Let S be the region between the graph of g and the xaxis on the interval [0,4]. Use a lefthand sum with 2 subintervals to estimate the area of S. Is this an underestimate or an overestimate? 
Example 4
Use a lefthand sum with 4 subintervals to estimate the area of W.

Example 5
Let f ( x ) = x^{2} + 2 and let R be the region between the graph of f and the xaxis on the interval [0,8]. Use a lefthand sum with 4 subintervals to estimate the area of R. 
Example 6
Let f ( x ) = 4x and let R be the region between the graph of f and the xaxis on the interval [1,2]. Use a lefthand sum with 4 subintervals to estimate the area of R. 
Example 7
Let f ( x ) = 2x on [2,10]. Find LHS(5). That is, use a lefthand sum with 5 subintervals to estimate the area between the graph of f and the xaxis on [2,10]. 
Example 8
Use a lefthand sum to estimate the area between the graph of g and the xaxis on the interval [0,10]. 