inn Annual coal production in the US in billion tons per yea

inn. Annual coal production in the US, in billion tons per year) is given in the fable mate the total amount of coal produced in the US between 1997 and 2009. If f(t) is the rate of eoal production t years since or 1997, write a integral to represent the 1997-2009 coal uction. Year 1997 1999 2001 2003 2005 2007 2009 Rate 1.090 1.094 1.121 1.072 1.132 1.147 1.073 Adis Press, 1976). Accessed May 2011.

Solution

t is nothing but the time interval between two successive years.For example the years are at equal intervals of 2 years (1997,1999,2001,2003.....).This t can also be calculated by number of years in between 1997-2009 divided by number of years considered i.e 14/7=2=t.

First , calculating the left hand sum=t(1.090+1.094+1.121+1.072+1.132+1.147)=13.312

Then,

calculating the right hand sum=t(1.094+1.121+1.072+1.132+1.147+1.073)=13.278

So, The amount of coal production according to left hand sum=13.312

   right hand sum=13.278