Studied by 2 peopleVolume using cross-sectional area
∫ from a to b of A(x)dx
Volume using disc method
∫ from a to b of π(f(x)²)dx
Volume using washer method
∫ from a to b of π(f(x)²-g(x)²)dx
Length of an unparameterized curve
∫ from a to b of √(1 + f’(x)^2)dx
Work if force is constant
force * distance
Work if force = F(x)
∫ from a to b of F(x)dx
Work needed to stretch spring from x=a to x=b
∫ from a to b of F(x)dx
Work needed to pump water from a to b
∫ from a to b of 62.5A(x)(l-x)dx
bar x
(∫ from a to b of x(f(x)-g(x))dx) / A
bar y
(∫ from a to b of 1/2(f(x)^2-g(x)^2)dx) / A
Pappus’ Theorem
V = 2πbA
Length of parameterized curve
∫ from t₀ to t₁ of √(x’(t)²+y’(t)^2)dt
Note
Flashcard