So far as I have learned,

one has to integrate the curve f(x) function only in order to find the area under the curve.

But I Quote as follows:

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The volume

of the liquid in a container leaks out at the rate of

where

is the time in seconds.

Find the amount of liquid lost in the third second.

*Solution ...* (decreasing)

The third second is between

and

.

So we find (value of

when

)

(value of

when

using a definite integral.

Change of volume =

Hence

of liquid was lost in the third second.

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According to me, one should integrate the gradient function back to the curve function and then integrate again as usual to find area.

So,

Equation of Curve =

Arbitrary constant C may be ignored as t=0 when V=0 for physical variables.

Therefore,

Change of Volume between

and

The volume lost must be 95 , How far do you agree?