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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

If oil leaks from a tank at a rate of r(t) gallons per minute at time t, what does 0 120 r ( t ) d t represent?

To determine

To represent: The integral function 0120r(t)dt.

Explanation

Given information:

The rate of oil leaked from the tank is r(t).

The integral function is 0120r(t)dt (1)

The net change theorem is shown below:

abF'(x)dx=F(b)F(a)

Here, the rate of change of the function [y=F(x)] with respect to x is F'(x) and x changes from a to b as F(b)F(a).

The rate of oil leaks from the tank is shown as r(t).

Assumption:

The volume of oil present at time t as V'(t).

The negative sign represents decrease of volume due to oil leakage

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