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Question Number 80914 by TawaTawa last updated on 07/Feb/20

(1)  Integrate  F(x, y)  =  x^2    over the region bounded by   y  =  x^2 ,  x  =  2  and x  =  1    (2)  Integrate    G(x, y)  =  x^2  + y^2     over the region bounded by the   triangle    x  =  y,  y  =  1  and  y  =  0

$$\left(\mathrm{1}\right) \\ $$$$\mathrm{Integrate}\:\:\mathrm{F}\left(\mathrm{x},\:\mathrm{y}\right)\:\:=\:\:\mathrm{x}^{\mathrm{2}} \:\:\:\mathrm{over}\:\mathrm{the}\:\mathrm{region}\:\mathrm{bounded}\:\mathrm{by}\:\:\:\mathrm{y}\:\:=\:\:\mathrm{x}^{\mathrm{2}} , \\ $$$$\mathrm{x}\:\:=\:\:\mathrm{2}\:\:\mathrm{and}\:\mathrm{x}\:\:=\:\:\mathrm{1} \\ $$$$ \\ $$$$\left(\mathrm{2}\right) \\ $$$$\mathrm{Integrate}\:\:\:\:\mathrm{G}\left(\mathrm{x},\:\mathrm{y}\right)\:\:=\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:\:\:\:\mathrm{over}\:\mathrm{the}\:\mathrm{region}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\: \\ $$$$\mathrm{triangle}\:\:\:\:\mathrm{x}\:\:=\:\:\mathrm{y},\:\:\mathrm{y}\:\:=\:\:\mathrm{1}\:\:\mathrm{and}\:\:\mathrm{y}\:\:=\:\:\mathrm{0} \\ $$

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