MATH 32B Lecture Notes - Lecture 1: Riemann Sum, Iterated Integral
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Integration in 2 variables ffp fix , y l da " signed volume. Let d be the rectangle [ aib ] x cold ] d - f : pt ir f : " signed area single variable fab fly , dx. Estimate for total signed area oxo = xi - xi- i and height f ( pit height f ( pi ; ) = f ( p ! Ri; = [xi - i , xi ] x [ y ; - i , 4 ;] and. S n , m = i i ftp. o-1. ox-o . [ = i 5=1 ( riemann sum ) The double integral of fix , y ) over the rectangle r is. Max { oxi , oy , } If the limit exists , we say f is integrable on r ext flx , y ) = xz -1 y riemann sum 52,2 on r= [ 0,2 ] x [ 0,2] ( any sample point )
