Use right and left endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. f(x) = 2x + 2, [0, 2], 4 rectangles Step 1 To find two approximations of the area of the region between the graph of the function f(x) = 2x + 2 and the x-axis over the interval [0, 2] using 4 rectangles, first partition the interval [0, 2 ] into n = | Then the width of each rectangle is given by using the following formula. b-a Ax= Step 2 Therefore, the width of each rectangle is b-a n Ax = n 4 -0.5 2 - 0 Step 3 Consider the right endpoints approximation of the area of the region. Observe the region between the graph of the function f(x) = 2x + 2 and the x-axis over the interval [0, 2] with four circumscribed rectangles, which is shown below. 1 6 4 0.5 1.0 1.5 The right endpoints of the n intervals are Ax(i) where i = 1 to 4 Thus, the right end points of four intervals are Ax(i) = 2 2.0 Then substitute 4x ==-- and n = 4 to find the left end points of four intervals. 1 That is, the four right end points of the intervals are Therefore, the four intervals are given as follows. ·[글·ㄷ 2 2.5 1 (i), wherei 1 to 4. 1, 2 2 X and 2. (222) 4 subintervals.
Use right and left endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. f(x) = 2x + 2, [0, 2], 4 rectangles Step 1 To find two approximations of the area of the region between the graph of the function f(x) = 2x + 2 and the x-axis over the interval [0, 2] using 4 rectangles, first partition the interval [0, 2 ] into n = | Then the width of each rectangle is given by using the following formula. b-a Ax= Step 2 Therefore, the width of each rectangle is b-a n Ax = n 4 -0.5 2 - 0 Step 3 Consider the right endpoints approximation of the area of the region. Observe the region between the graph of the function f(x) = 2x + 2 and the x-axis over the interval [0, 2] with four circumscribed rectangles, which is shown below. 1 6 4 0.5 1.0 1.5 The right endpoints of the n intervals are Ax(i) where i = 1 to 4 Thus, the right end points of four intervals are Ax(i) = 2 2.0 Then substitute 4x ==-- and n = 4 to find the left end points of four intervals. 1 That is, the four right end points of the intervals are Therefore, the four intervals are given as follows. ·[글·ㄷ 2 2.5 1 (i), wherei 1 to 4. 1, 2 2 X and 2. (222) 4 subintervals.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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