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Use Theorem 9.13 to show that the area of the circle defined by the polar equation r=ais πa2.

Short Answer

Expert verified

The area of the circle isπa2

Step by step solution

01

Step 1. Given Information

The given function of the circle isr=a.

02

Step 2. Use the formula for area of a region bounded by a curve

  • The region is bounded by the curve r=a.
  • The region is a circle, so the boundary arcs will be θ=0,θ=2π.
  • So, the area of the region will be calculated as follows:role="math" localid="1649917065658" 1202πa2dθ=a2202πdθ=a22×2π=πa2
  • Hence, the area of the curve isπa2.

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