Find the average value of the function 𝑓(𝑥) = √𝑥 on the interval [4, 9].

Answer 1

integral of sqrx = (x^3/2)/(3/2) = (2/3)(x^3/2)

from 4 to 9, the integral = (2/3)[9^3/2 - 4^3/2] = (2/3)(27-8) = (2/3)(19 = 38/3

divide by 9-4 or 5

average = 38/15

the integral sign is a type of "S" shape, which stands for sum. It's the same as the capital Greek Sigma sign which stands for sum, but the integral is the sum of infinitely small numbers.

An average is the sum of numbers divided by the total interval of numbers

Answer 2

Average value of a function f(x) over the interval [a.b]

= 1/(b-a)∫_a^b f(x) dx; f(x) = √x ;

In this case it is = 1/(9-4) .2/3.[ [9]^3/2 - [4]^3/2 ] = 1/5.2/3.[27-8]= 38/15 Ans.

Answer 3

The average is the sum of the numbers divided by the number of numbers.

In this case, to find the sum of the numbers, we use and integral:

₄∫⁹√x dx = 38/3 (you can integrate manually by finding the antiderivative and plugging in the limits of integration or use a calculator)

The number of numbers is 9 - 4 = 5

So the average = (38/3)/5 = 38/15