About: Formula for Area Bounded by a Circle/Proof   Sponge Permalink

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Which yields the upper half of the circle on the domain interval . Let represent the area of the circle. Then, Our integral resists solution as is, impeded by the radical. Note that . Equivalently: Substituting the trigonometric identity into the integral, we obtain: Which cannot be evaluated without changing the variable of integration. Beginning with: Substituting back into the integral and taking care to change the interval of integration, we arrive at: QED

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  • Formula for Area Bounded by a Circle/Proof
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  • Which yields the upper half of the circle on the domain interval . Let represent the area of the circle. Then, Our integral resists solution as is, impeded by the radical. Note that . Equivalently: Substituting the trigonometric identity into the integral, we obtain: Which cannot be evaluated without changing the variable of integration. Beginning with: Substituting back into the integral and taking care to change the interval of integration, we arrive at: QED
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abstract
  • Which yields the upper half of the circle on the domain interval . Let represent the area of the circle. Then, Our integral resists solution as is, impeded by the radical. Note that . Equivalently: Substituting the trigonometric identity into the integral, we obtain: Which cannot be evaluated without changing the variable of integration. Beginning with: Substituting back into the integral and taking care to change the interval of integration, we arrive at: QED
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