Question Number 189335 by Gbenga last updated on 14/Mar/23
$$\boldsymbol{\mathrm{determine}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{volume}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{region}}\: \\ $$$$\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{between}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{xy}}\:\boldsymbol{\mathrm{plane}} \\ $$$$\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}}\right)=\mathrm{2}+\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{above}} \\ $$$$\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{triangle}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{vertices}}\:\left(\mathrm{0},\mathrm{0}\right),\left(\mathrm{6},\mathrm{0}\right)\: \\ $$$${a}\boldsymbol{{nd}}\:\left(\mathrm{6},\mathrm{2}\right)\:\boldsymbol{{using}}\:\boldsymbol{{double}}\:\boldsymbol{{integral}} \\ $$