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Answer by Gaurang Tandon for Integrating the area of a circle with rectangles

What makes you think it is incorrect? Do not forget that:$$2\cdot\int\sqrt{1-x^2}=x\sqrt{1-x^2}+\sin^{-1}x$$Have a look here if you're forgotten the derivation.

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Integrating the area of a circle with rectangles

I've been wondering if there was another way of calculating the area of a circle by integration, other than using trig substitution. So I decided to try dividing the circle into many rectangles, and...

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