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Unit 8: Applications of Integration

AP Calculus BC — Note Packet

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Key Terms

Arc Length

The length of a _ curve, found by integrating infinitesimally small segments.

Surface Area of Revolution

The area of a 3D surface created by _ a curve around an axis, calculated by integrating 2π * (radius) * ds.

Parametric Integration

Adapting standard integration formulas (like area under a curve) when x and y are both defined by a third _ 't'.

Polar Area Formula

The formula A = (1/2)∫r²dθ used to find the area enclosed by a polar curve, by summing tiny _ of a circle.

Polar Arc Length

The formula L = ∫ √(r² + (dr/dθ)²) dθ used to find the length of a curve defined in _ coordinates.

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