Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
The value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)
What is integration?
It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
The parametric equations for the line segment from (0, 0, 0) to (2, 3, 4)
x(t) = (1-t)0 + t×2 = 2t
y(t) = (1-t)0 + t×3 = 3t
z(t) = (1-t)0 + t×4 = 4t
Finding its derivative;
x'(t) = 2
y'(t) = 3
z'(t) = 4
The line integral is given by:
[tex]\rm \int\limits_C {xe^{yz}} \, ds = \int\limits^1_0 {2te^{12t^2}} \, \sqrt{2^2+3^2+4^2} dt[/tex]
[tex]\rm ds = \sqrt{2^2+3^2+4^2} dt[/tex]
After solving the integration over the limit 0 to 1, we will get;
[tex]\rm \int\limits_C {xe^{yz}} \, ds = \dfrac{\sqrt{29}}{12} (e^{12}-1)[/tex] or
= 73037.99 ≈ 73038
Thus, the value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)
Learn more about integration here:
brainly.com/question/18125359
#SPJ4
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
