AP Calc Unit 8: Applications of Integrals

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16 Terms

1
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Average Value Theorem

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Integral of Acceleration

Velocity

<p>Velocity</p>
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Integral of Velocity

Position

<p>Position </p>
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Total Distance

∫|v(t)| dt

  • w/o absolute value: total displacement

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How do you find final value?

Final Value = Initial + Change

s(b) = s(a) + ∫ v(t) dt

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Area Between Curves: In terms of x

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Area Between Curves: In terms of y

∫ (f(y) - g(y)) dt

  • right-left

8
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How do you find cross sections?

  • Use the area formula based on the shape of the cross section

  • Use f(x)-g(x) as your s/r

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Cross Sections: Area of Squares

s²

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Cross Sections: Area of Triangles

½ bh

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Cross Sections: Area of Semicircles

½πr²

  • r= f(x)-g(x)/2

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Cross Sections: Area of Equilateral Triangles

√3/4s2

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Cross Sections: Area of Rectangles

bh

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Disk Method

  • Used with only ONE function: when it touches the x-axis

<ul><li><p>Used with only ONE function: when it touches the x-axis</p></li></ul><p></p>
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Washer Method

  • Used with TWO functions: when space b/t x-axis

<ul><li><p>Used with TWO functions: when space b/t x-axis </p></li></ul><p></p>
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Cross Sections: Isosceles Right Triangle

½ L²