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Question Number 189335 by Gbenga last updated on 14/Mar/23

determine the volume of the region   that is between the xy plane   and f(x,y)=2+cos(x^2 ) and is above   the triangle with vertices (0,0),(6,0)   and (6,2) using double integral

$$\boldsymbol{\mathrm{determine}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{volume}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{region}}\: \\ $$$$\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{between}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{xy}}\:\boldsymbol{\mathrm{plane}} \\ $$$$\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}}\right)=\mathrm{2}+\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{above}} \\ $$$$\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{triangle}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{vertices}}\:\left(\mathrm{0},\mathrm{0}\right),\left(\mathrm{6},\mathrm{0}\right)\: \\ $$$${a}\boldsymbol{{nd}}\:\left(\mathrm{6},\mathrm{2}\right)\:\boldsymbol{{using}}\:\boldsymbol{{double}}\:\boldsymbol{{integral}} \\ $$

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