Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Evaluate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C C is the line segment from (1, 0, 0) to (4, 1, 3)

Sagot :

akiran007

The line integral is the path of the function along a line having a continuous value.

The integral solved gives the value 111.

The given question is

[tex]\int\limits^c {z}^2 \, dx+ {x}^2 \, dy+ {y} ^2\, dz[/tex]

where C is the line from (1, 0, 0) to (4, 1, 3)

Here

x→ 1⇒ 4

y→  0⇒1

z→  0⇒ 3

Let  t be defined be the range  0≤ t ≤ 1

Then x= 4t+1   :    dx= 4dt

y= t                 ":   dy= dt

z= 3t                : dz= 3dt

Putting the values

[tex]\int\limits^1_0{9t^2} \, 4dt + \int\limits^1_0 {16t^2+1+8t} \, 3dt +\int\limits^1_0 {t^2} \,3dt[/tex]

=  [36(1)²- 36(0)²]+ 3 [16(1)² +1+8(1)] - 3 [16(0)² +1+8(0)]  + [3(1)²- 3(0)² ]

= 36 +75-3+3

= 111  

https://brainly.com/question/16571667

https://brainly.com/question/18762649

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.