Question

(1 point) Suppose the average value of f(x) on the interval (5,9) is 65. Calculate s ro f(x) dx. The integral equals Suppose a car travels in a straight line at an average velocity of 65 miles per hour. How far does the car travel from 5:00pm to 9:00pm? The car travels miles.

Answer 1

1)

$\text{ Average value of function }f(x) \text{ on the interval [a,b] is given by }$

$Average = \frac{1}{b-a} \int_a^b f(x)dx$

$\text{ Given that average value of }f(x ) \text{ on the interval [5,9] is 65 }$

= f(x)dx = 65

$=> \frac{1}{4} \int_5^9 f(x)dx =65$

$=> \int_5^9 f(x)dx =65(4)=260$

Hence,

$\text{ The integral equals }260$

2)

$\text{ Given average velocity is 65 miles per hour}$

$\text{Average velocity} =\frac{\text{ Total distance}}{\text{ time }}$

$=> \text{ Total distance} = \text{Average velocity} \times {\text{ time }}$

$\text{ Number of hours between 5.00pm to 9.00 pm } =4$

$=> \text{ Total distance} = 65 \times 4 =260$

Hence,

$\text{ The car travels 260 miles. }$