Q) Water flows into and out a storage tank. The following graph is is the record

Question

Q) Water flows into and out a storage tank. The following graph is is the recorded rate of change f(x) of the volume of water in the tank, in liters perday. if the amount of water in the tank at time=0 is 2000L ESTIMATE THE AMOUNT OF WATER IN THE TANK AFTER SIX DAYS.

Q) Water flows into and out a storage tank. The following graph is the recorded rate of change f(x) of the volume of water in the tank, in liters per day. if the amount of water in the tank at time t=0 is 2000L ESTIMATE THE AMOUNT OF WATER IN THE TANK AFTER SIX DAYS.

Explanation / Answer

because y = f(x) => rate of change in volume of water in tank

so integral between t =0 to t =6 will give the total change in volume in tank

so we have to estimate the integral (total sign area)

1) time t = 0 to t=2

we can take it as trapezoidal

A1 = 1/2 *(2+4) *2 = 6

2) t = 2 to t=3

this is a trapezoidal

A2= 1/2 * (4+2) *1 = 3

3) t = 3 to 4

by observation

A3 = 1/2 * ( 1 ) = 1/2

4) t = 4 to 6

again trapzodial

A4 = - 1/2* (1+3)*2 = -4

so total integration

A1 + A2 + A3 + A4 = 5.5

so total volume after t = 6 is 5500 Lt

at t = 0 volume is 2000 Lt

please ask if any doubt..but rate the answer i spent a lot of time

  

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