The graph of a function g is given a 4 Consider the integra

The graph of a function g is given a = 4 Consider the integral I when answering the following questions. I = Integral^12_-12 g(x) dx Estimate the integral I with six subintervals using right end points. R_6 =__________Estimate the integral I with six subintervals using left endpoints. L_6 =___________Estimate the integral I with six subintervals using midpoints.

Solution

Each bloch is 2 along x and 2 along y

Therefore, area of one block = 2*2 = 4

a) For this part we will the intersection points on the rigth side of each column grid. eg for -12,-10 column the right side touches at row 3. Thus 3 blocks are taken for integral.

Similarly we count the sum of number of blocks in each column:

3+2+0-1-2-3-3.5-3-2-1+1+5 = -4.5 blocks = -4.5*4 = -18

b) Similarly by taking the left side intersection we get the number of blocks as:

4+3+2+0-1-2-3-3.5-3-2-1+1 = -5.5 blocks = -5.5*4 = -22

c)Taking the midpoints we get:

3.5+2.5+1-0.5-1.5-2.5-3.25-3.25-2.5-1.5+0+3 = -5 blocks = -5*4 = -20