The document provides calculations to estimate the total cost of drilling at increasing depths. It calculates the costs from drilling at depths of $24/ft, $36/ft, $56/ft, and $84/ft, finding the total to be $146,000. It then uses trapezoids to estimate the cost, finding a higher estimate because the trapezoids include some area outside the curve. Using smaller trapezoids, it estimates the cost to be $144,500, which is closer to the actual cost.

1. $24/ft $84/ft.
The price increases because it is harder and slower to drill at increased depths.
500
10
28.4 squares x $5000/square = $142,000
T1 = (0.5)(1000)(24+36)
T2 = (0.5)(1000)(36+56)
T3 = (0.5)(1000)(56+84)
Ttotal = 1000[0.5(24) + 36 + 56 + 0.5(84)]
= $146,000
Overestimate
Higher, because trapezoids include small area outside of region under curve.
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2. T6 = $144,500
Higher, because trapezoids are still inscribed
under the concave curve.
R6 = $143,750
Yes, within $750.
$144,001.80 $144,000.07
$144,000.00
indefinite integral
20x + 1/3(0.000004)x3 + C
(165,333.333... + C) ­ (21,333.333... + C) = $144,000.00
Shazam!
It's Math Magic!
Same as conjecture!
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3. f(x) = x7 + C y = ­cos x + C
2x
u = 1 e + C v =
(4x+5)8
+ C
2 32
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