AP Calculus BC

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21 Terms

1
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shell method: revolved around y-axis

V=2π∫p(x)h(x)dx

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shell method: revolved around x-axis

V=2π∫p(y)h(y)dy

3
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arc length

L=∫√(1+(f’(x))²dx

4
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surface area: revolved around x-axis

S=2π∫f(x)√(1+(f’(x))²dx

5
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surface area: revolved around y-axis

S=2π∫x√(1+(f’(x))²dx

6
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work

W=∫F(x)dx

7
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Hooke’s Law

F=kx

8
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Newton’s Law

F=C/x²

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Boyle’s Law

P=k/V

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mass

m=force/acceleration

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moment

moment=mass∙distance

12
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moment about the origin: one-dimensional system

M0=m1x1+…+mnxn

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moment about the y-axis: two-dimensional system

My=m1x1+…+mnxn

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moment about the x-axis: two-dimensional system

Mx=m1y1+…+mnyn

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center of mass: two-dimensional system

(x̄=My/m,ȳ=My/m) where m=m1+…+mn

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moment about the y-axis: planar lamina

My=∫x(f(x)-g(x))dx

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moment about the x-axis: planar lamina

Mx=∫((f(x)+g(x))/2)(f(x)-g(x))dx

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center of mass: planar lamina

(x̄=My/m,ȳ=My/m) where m=∫(f(x)-g(x))gx

19
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pressure

P=density∙depth

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fluid force on a horizontal surface

F=pressure∙area

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force exerted by a force

F=∫h(y)L(y)dy