5 years ago

We approximate the volume under f(x,y) over the region where 0≤x≤3 and 0≤y≤2.
The volume is approximated in a Riemann Sum of 6 rectangular prisms and visualized in calcplot3D.

The process of taking a difficult problem and cutting it up into smaller easier problems is also discussed, as we find the volume of this solid by cutting it up into 6 rectangular columns. The underestimate is discussed. Each of the six volumes are calculated by find the length, width and height of each prism. The volumes are then summed and the graphic and approximated volume are concurrently shown in CalcPlot3D.

Finally, the next video is introduced within the context of finding a more accurate volume of the solid.

The link to the calcplot3D visualization is here:
https://c3d.libretexts.org/CalcPlot3D/index.html?type=region;region=x;visible=true;alpha=150;view=0;top2d=2;bot2d=0;umin=0;umax=3;top3d=24-x^2-3y^2;bot3d=0;grid=25,25;showriemann=true;xnum=3;ynum=2;partition=Inner;heightpt=4;showpts=false;mode=rect;polarform=t;polartop=2;polarbottom=0;polarmin=%CF%80/4;polarmax=3%CF%80/4&type=window;hsrmode=0;nomidpts=true;anaglyph=-1;center=8.479206834744925,4.8370832491824665,2.169257267842504,1;focus=0,0,0,1;up=-0.250790730365395,-0.20113018118593123,0.9469163953480297,1;transparent=false;alpha=140;twoviews=false;unlinkviews=false;axisextension=0.7;xaxislabel=x;yaxislabel=y;zaxislabel=z;edgeson=true;faceson=true;showbox=false;showaxes=true;showticks=true;perspective=true;centerxpercent=0.39645639607941685;centerypercent=0.5526315789473687;rotationsteps=30;autospin=true;xygrid=false;yzgrid=false;xzgrid=false;gridsonbox=false;gridplanes=false;gridcolor=rgb(128,128,128);xmin=-1;xmax=4;ymin=-1;ymax=4;zmin=-1;zmax=5;xscale=1;yscale=1;zscale=1;zcmin=-4;zcmax=4;zoom=0.627556;xscalefactor=1;yscalefactor=1;zscalefactor=0.1

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