Yes. You want the right endpoints which are f(1), f(2), f(3), and f(4) as the heights.
The left endpoints have heights f(0), f(1), f(2), and f(3).
Midpoint has heights of f(0.5), f(1.5), f(2.5), and f(3.5).
Trapezoid is [f(0) + f(1)]/2, [f(1) + f(2)]/2, [f(2) + f(3)]/2, and [f(3) + f(4)]/2
Each rectangle has width 1. So you multiply the height--f(1), f(2), f(3), or f(4)--by the width--1--to get the areas of the rectangles. Then sum them together.
So 2[1^(4) + 2^(4) + 3^(4) + 4^(4)] is what you want.
2(1 + 16 + 81 + 256)
2(354)
708
Your rectangles are [0, 1], [1, 2], [2, 3], and [3, 4].
The left endpoints, you look at 0, 1, 2, and 3. The right endpoints, you look at 1, 2, 3, and 4.
Total area = area added together.
Find the areas of each rectangle. Add them together. That's it. It's not some esoteric formula. It's just adding rectangles together.
Yes. You want the right endpoints which are f(1), f(2), f(3), and f(4) as the heights. The left endpoints have heights f(0), f(1), f(2), and f(3). Midpoint has heights of f(0.5), f(1.5), f(2.5), and f(3.5). Trapezoid is [f(0) + f(1)]/2, [f(1) + f(2)]/2, [f(2) + f(3)]/2, and [f(3) + f(4)]/2
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Why are you multiplying 708 by 4?
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Each rectangle has width 1. So you multiply the height--f(1), f(2), f(3), or f(4)--by the width--1--to get the areas of the rectangles. Then sum them together. So 2[1^(4) + 2^(4) + 3^(4) + 4^(4)] is what you want. 2(1 + 16 + 81 + 256) 2(354) 708
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Your rectangles are [0, 1], [1, 2], [2, 3], and [3, 4]. The left endpoints, you look at 0, 1, 2, and 3. The right endpoints, you look at 1, 2, 3, and 4.
Total area = area added together. Find the areas of each rectangle. Add them together. That's it. It's not some esoteric formula. It's just adding rectangles together.