Area and volume of cross sections between curves

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Calculus

Integration

AP Calculus BC

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10 Terms

1
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Coefficient of semi-circle

Pi/8

2
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Coefficient of square

1

3
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Isosceles right triangle (side x is a leg) coefficient

1/2

4
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Isosceles right triangle (side x is hypotenuse) coefficient

1/4

5
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Equilateral triangle coefficient

(Sqrt(3))/4

6
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Rectangle

K∫(f-g)2dx or ∫h(x)(f-g)dx

7
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Washer/disk

Pi∫(f(x))2 - (g(x))2 dx

8
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Shell

2pi∫r(x)(f(x)-g(x))dx

9
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Arc length

∫Sqrt(1+f’(x))dx

10
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Surface Area

2pi∫r(x)Sqrt(1+f’(x))dx