How Do I Calculate the Area of a Sector with Different Lengths?

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SUMMARY

The discussion focuses on calculating the area of a sector of a circle when the radius varies. The formula provided for this calculation is 1/2 ∫(α to β) f(θ)² dθ, utilizing polar coordinates. This approach allows for the integration of varying radius lengths within the specified angle limits. Clarification on the specific nature of the lengths is necessary for accurate application of the formula.

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  • Understanding of polar coordinates
  • Basic knowledge of calculus, specifically integration
  • Familiarity with sector geometry
  • Concept of variable radius in circular shapes
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  • Study polar coordinate systems in detail
  • Practice integration techniques for varying functions
  • Explore geometric properties of sectors and arcs
  • Learn about applications of calculus in real-world scenarios
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Students in mathematics, engineers working with circular designs, and anyone interested in advanced geometry and calculus applications.

mathelord
how do i find the area of a shape like a sector,but having different lenghts
 
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A sector of a circle? By different lengths, do you mean the radius varies? If that is what you mean, you could use polar coordinates in which the area would be:

\frac{1}{2}\int_{\alpha}^{\beta}f(\theta)^{2}d\theta

I don't know if this is exactly what you are asking, so maybe someone else can clear it up.
 

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