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Nuetrik [128]
2 years ago
9

Evaluate the line integral, where c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

Mathematics
1 answer:
Arada [10]2 years ago
7 0

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)

<h3>What is integration?</h3>

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:

\rm \int\limits_C {xe^{yz}} \, ds = \int\limits^1_0 {2te^{12t^2}} \, \sqrt{2^2+3^2+4^2} dt

 

\rm ds = \sqrt{2^2+3^2+4^2} dt

After solving the integration over the limit 0 to 1, we will get;

\rm \int\limits_C {xe^{yz}} \, ds = \dfrac{\sqrt{29}}{12}  (e^{12}-1)   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

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