MAT 103 Assignment Problem 5.3

MAT 103 Assignment Problem 5.3 | Borough of Manhattan Community College

5.3 Riemann Sums And Definite Integrals 

Question 1

(1 point) The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x)=−x25+2xf(x)=−x25+2x on the interval [2,6][2,6].
The value of this left endpoint Riemann sum is 17.7 , and this Riemann sum is       [select an answer] an overestimate of equal to an underestimate of there is ambiguity  the area of the region enclosed by y=f(x)y=f(x), the x-axis, and the vertical lines x = 2 and x = 6.

Question 2

(1 point) Consider the integral

∫84(3x+5)d

Question 3

(1 point)

Evaluate the definite integral ∫0−22x∫−202x dxdx as a limit.

Question 4

(1 point) Suppose ∫−5−8f(x)dx=2, ∫−7−8f(x)dx=2, ∫−5−6f(x)dx=10∫−8−5f(x)dx=2, ∫−8−7f(x)dx=2, ∫−6−5f(x)dx=10.

Question 5

1 point) Using Properties of Definite Integrals.
Given ∫3−3f(x)∫−33f(x) dx=0dx=0   and   ∫30f(x)∫03f(x) dx=4

Question 6

(1 point) Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using high school geometry.

Question 7

(1 point) Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using high school geometry.

Question 8

(1 point) Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using high school geometry.

Question 9

(1 point) Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using high school geometry.