Why we sometimes take the area bounded by the curve is sum of positive area and absolute of negative area(e.g. ∫\int_0^2π sin(x)\, dx is equal to 4 or area of ellipse )?But sometimes we just sum positive and negative areas which is equal to 0(e.g. area of cycloid →when we integrate we get r*r(x-2sin(x)+½x+sin(2x)/4) from 0 to 2π and we get r*r(2π-2*0+π+0)-0=3r*r*π).Why I can´t just take for -2sin(x) from 0 to 2π is equal to 4 and equally for sin(2x)/4,because that is the area bounded by the curve?(adsbygoogle = window.adsbygoogle || []).push({});

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# Sum of area bounded by the curve

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