5.5.2 average value of sqrt{x} [0,4]

In summary, the average value of the function $\sqrt{x}$ on the interval $[0,4]$ is $\dfrac{4}{3}$. You can post this problem on LinkedIn and also mention that you suggest people come here for any additional tips or advice.
  • #1
karush
Gold Member
MHB
3,269
5
$\tiny{s8.5.5.2}$
Find the average value of the function on the given interval. $\sqrt{x}\quad [0,4]$
average value $\boxed{f_{ave}=\dfrac{1}{b-a}\int_a^b f(x) \ dx}$
so with $a=0$ and $b=4$ thus
$\dfrac{1}{4-0}\displaystyle\int_0^4 \sqrt{x} \ dx
\implies =\dfrac{1}{4}\left[\dfrac{2}{3}x^{\dfrac{3}{2}}\right]^4_0
\implies = \dfrac{1}{4}\dfrac{16}{3}=\dfrac{4}{3}$

ok, I think this is correct, but possible typos
I want to poIst this problem on Linkedin this week so if there is any added tips
i will add it in... been getting lots of views on IN even tho it is not essentually a math forum
of I Suggest they come here
 
Physics news on Phys.org
  • #2
Yes, that is correct
 

FAQ: 5.5.2 average value of sqrt{x} [0,4]

1. What is the average value of sqrt{x} on the interval [0,4]?

The average value of sqrt{x} on the interval [0,4] is 2.

2. How do you calculate the average value of sqrt{x} on the interval [0,4]?

To calculate the average value of sqrt{x} on the interval [0,4], you can use the formula: 1/(b-a) * integral from a to b of sqrt{x} dx, where a=0 and b=4.

3. What is the significance of finding the average value of sqrt{x} on the interval [0,4]?

The average value of sqrt{x} on the interval [0,4] represents the average height of the graph of sqrt{x} on the interval. This value can be useful in understanding the overall behavior of the function on the given interval.

4. Can the average value of sqrt{x} on the interval [0,4] be negative?

No, the average value of sqrt{x} on the interval [0,4] cannot be negative as the function sqrt{x} is always positive on this interval.

5. How does the average value of sqrt{x} on the interval [0,4] compare to the average value of x on the same interval?

The average value of sqrt{x} on the interval [0,4] is smaller than the average value of x on the same interval. This is because the function sqrt{x} is concave down and thus, the average value of sqrt{x} will be closer to the minimum value of the function on the interval.

Similar threads

Replies
1
Views
926
Replies
3
Views
1K
Replies
3
Views
1K
Replies
3
Views
1K
Replies
5
Views
2K
Replies
5
Views
1K
Back
Top