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\(\int_{}^{}\int_{}^{}\)π‘₯2+ 𝑦2 𝑑𝐴; 𝑅 ={ ( π‘₯, 𝑦 ) | βˆ’1 ≀ π‘₯ ≀ 1, 0 ≀ 𝑦 ≀ 2 }

 Mar 22, 2017
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That means \(\displaystyle\int^{2}_{0}\int^{1}_{-1}x^2+y^2 dx dy\)

\(\displaystyle\int^{2}_{0}\int^{1}_{-1}x^2+y^2 dx dy\\ =\displaystyle\int^{2}_{0}\left[\dfrac{x^3}{3}+xy^2\right]^{1}_{-1}dy\\ =\displaystyle\int^{2}_{0}\left(\dfrac{2}{3}+2y^2\right)dy\\ =\left[\dfrac{2y}{3}+\dfrac{2y^3}{3}\right]^{2}_{0}\\ =\dfrac{20}{3}\)

 Mar 23, 2017

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