#### To determine

**To find:**

The lower and upper estimates for the total amount of oil leaked

#### Answer

Upper estimate *=70* liters

Lower estimate *=63.2* liters

#### Explanation

**1) Concept:**

The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles:

*A=limn→∞∑i=1nfxi∆x*

where,

*∆x=b-an & xi=a+i∆x*

2) **Calculation:**

It is given that an interval *0, 10* and *n=5*

That means

*a=0, b=10*

*∆x=b-an=10-05=2*

Upper estimate for the total amount of oil leaked

*L=∑i=0n-1fxi∆x*

*=2(8.7+7.6+6.8+6.2+5.7)*

*=2(35)*

*=70* liters

Lower estimate for the total amount of oil leaked

*R=∑i=1nfxi∆x*

*=2(7.6+6.8+6.2+5.7+5.3)*

*=231.6*

*=63.2* liters

**Conclusion:**

Upper estimate for the total amount of oil leaked is

*=70* liters

Lower estimate for the total amount of oil leaked is

*=63.2* liters