MATH141 Exam 1 Formulas
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Last updated 3:40 AM on 2/7/23
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12 Terms
1
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Volume using cross-sectional area
∫ from a to b of A(x)dx
2
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Volume using disc method
∫ from a to b of π(f(x)²)dx
3
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Volume using washer method
∫ from a to b of π(f(x)²-g(x)²)dx
4
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Length of an unparameterized curve
∫ from a to b of √(1 + f’(x)^2)dx
5
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Work if force is constant
force \* distance
6
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Work if force = F(x)
∫ from a to b of F(x)dx
7
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Work needed to stretch spring from x=a to x=b
∫ from a to b of F(x)dx
8
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Work needed to pump water from a to b
∫ from a to b of 62.5A(x)(l-x)dx
9
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bar x
(∫ from a to b of x(f(x)-g(x))dx) / A
10
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bar y
(∫ from a to b of 1/2(f(x)^2-g(x)^2)dx) / A
11
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Pappus’ Theorem
V = 2πbA
12
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Length of parameterized curve
∫ from t₀ to t₁ of √(x’(t)²+y’(t)^2)dt
