total change theorem. the integral of a rate change is the total change
Post on 31-Dec-2015
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Total Change Theorem
The integral of a rate change is the total change
'( ) ( ) ( )b
af x dx F b F a
If V’(t) is the rate that water flows into a lake at time t, then
shows the total volume of water that flows into the lake between t1 and t2
2
1
'( )t
tV t dt
Example
If the rate of a reaction (concentration change/sec) is given by C’(t), then what does the integral below represent?
2
1
'( )t
tC t dt
A particle moves along a line so that its velocity at time t is v(t) = t2 – t – 6. What is the displacement of the particle between 1 and 4 seconds?
The rate of disbursement of a 2 million dollar federal grant is proportional to the square of 100 –t where t is measured in days.
A) Find the total disbursed between 20 and 30 days
B) Find the amount that remains to be disbursed after 50 days.
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