At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
The value of the integral is [tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]
How to evaluate the integral?
The expression is given as:
[tex]\int\limits^{}_s {9x + 2y + z^2} \, dS[/tex]
[tex]x^2 + y^2 + z^2 = 1[/tex]
Rewrite the integral as:
[tex]\int\limits^{}_s {9x + 2y + z*z} \, dS[/tex]
As a general rule, we have:
[tex]\int\limits^{}_s {Px + Qy + R*z} \, dS[/tex]
By comparison, we have:
P = 9
Q = 2
R = z
By the divergence theorem, we have:
F = Pi + Qj + Rk
So, we have:
F = 9i + 2j + zk
Differentiate
F' = 0 + 0 + 1
F' = 1
The volume of a sphere is:
[tex]V = \frac{4}{3}\pi r^3[/tex]
Where:
r = F' = 1
So, we have:
[tex]V = \frac{4}{3}\pi (1)^3[/tex]
Evaluate
[tex]V = \frac{4}{3}\pi[/tex]
This means that:
[tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]
Hence, the value of the integral is [tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]
Read more about divergence theorem at:
https://brainly.com/question/17177764
#SPJ1
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.