# A log 10 m long is cut at 1 meter intervals and itscross-sectional areas A (at a distance x from theend of the log) are listed in the table. Use the M

A log 10 m long is cut at 1 meter intervals and itscross-sectional areas A (at a distance x from theend of the log) are listed in the table. Use the Midpoint Rule withn $=5$ to estimate the volume of the log. (in ${m}^{3}$ )

Show transcribed image text A log 10 m long is cut at 1 meter intervals and itscross-sectional areas A (at a distance x from theend of the log) are listed in the table. Use the Midpoint Rule withn $=5$ to estimate the volume of the log. (in ${m}^{3}$)

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Raheem Donnelly

interval 1 (0,2) midpoint area $=.65$ Volume $=2\cdot .65=1.3$
interval 2 (2,4) midpoint area $=.61$ ${m}^{2}$ Volume $=2\cdot .61=1.22$ ${m}^{3}$
interval 3 (4,6) midpoint area $=.59$ ${m}^{2}$ Volume $=2\cdot .59=1.18$ ${m}^{3}$
interval 4 (6,8) midpoint area $=.55$ ${m}^{2}$ Volume $=2\cdot .55=1.10$ ${m}^{3}$
interval 5 (8,10) midpoint area $=.50$ ${m}^{2}$ Volume $=2\cdot .50=1.00$ ${m}^{3}$
Total Volume $=1.3+1.22+1.18+1.10+1.00=5.80$ ${m}^{3}$