Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

(1 point) a) The rectangles in the graph belowilustrate a left endpoint Riermann

ID: 2891603 • Letter: #

Question

(1 point) a) The rectangles in the graph belowilustrate a left endpoint Riermann surm for f(z) =on the interval , Riemann sumforf(r)-11on the interval 201 b) The rectanglesinthegraph below illustrate a The value of this Riemann sum is overestimate of right endpoint 2,6 The value of this Riemann sum is and this Riemann sum is an and this Riemann sum is an underestimate of , earea of the re on enclosed by y- r the xads and the vertalines x : 2 and x-6 the area of the rein enclosed by y = r the x-ax s and the vert callines ?and x-6 . Left endpoint Riemann sum for y- on Right endpoint Riemann sum for y o 2.6

Explanation / Answer

Riemann left end point sum = x[f(x0) + f(x0 +x)....f(x0+7x)]

x = 0.5

=0.5[f(2) +f(2.5)+f(3)+f(3.5)+f(4)+f(4.5)+f(5)+f(5.5)]

=0.5[(2^2 /11) + (2.5^2 /11 )+ (3^2/11)+(3.5^2/11) +( 4^2/11)+( 4.5^2/11) +(5^2/11) + (5.5^2/11)]

= 123/22 (underestimate)

Riemann right end point sum= x[f(x0 +x)....f(x0+8x)]

x = 0.5

=0.5[f(2.5)+f(3)+f(3.5)+f(4)+f(4.5)+f(5)+f(5.5)+f(6)]

=0.5[(2.5^2 /11 )+ (3^2/11) +(3.5^2/11)+( 4^2/11 )+( 4.5^2/11) +(5^2/11) + (5.5^2/11) + (6^2/11)]

=155/22(overestimate)