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31 August, 19:02

Estimate the area under the curve f (x) = x2 + 1 from x = 0 to x = 6 by using three circumscribed (over the curve) rectangles. Answer to the nearest integer.

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  1. 31 August, 19:13
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    1) split the range in three identical invervals of size [6 - 0] / 3 = 2

    2) form three rectangles

    2a) First rectangle: base 2, height f (2) = 2^2 + 1 = 5

    area 1 = base * height = 2 * 5 = 10

    2b) second rectangle: base 2, height f (2+2) = 4^2 + 1 = 17

    area 2 = 2 * 17 = 34

    2c) third rectangle: base 2 height f (4+2) = 6^2 + 1 = 37

    area 3 = 2*37 = 74

    3) total area = area 1 + area 2 + area 3 = 10 + 34 + 74 = 118
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