CalculateSf(F(t)) | (t)] dzf[{T+Y(x+y+z) ds where C is the helix r(t) = (cos(t), sin(t), t). Let 0 ≤ t ≤T.

Answered: Calculate Sf(F(t)) | (t)) dt f √ √ √x +…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

Calculate
Sf(F(t)) | (t)] dz
f
[{T+Y
(x+y+z) ds where C is the helix r(t) = (cos(t), sin(t), t). Let 0 ≤ t ≤T.

Expert Solution

Step 1

What is Line Integral:

A line integral in mathematics is an integral in which the function to be integrated is assessed along a curve. Additionally, the phrases contour integral and path, curve, and curvilinear integral are used. However, line integrals in the complex plane are normally the only ones that utilise the term contour. The function that needs to be integrated could be a vector or scalar field. The line integral's value is the total of the field's values at each point along the curve, weighted by a scalar function.

Given:

Given line integral is

$\int_{C} (x + y + z) d s$

Here, $C$ is the helix $r (t) = <\cos t, \sin t, t>, 0 \leq t \leq π$ .