# Vector fields

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Let a vector field F be given by

F(x,y,z) = (x^3)i - (y^2)j + (2yz)k

and a curve C be given by

r(t) = 2ti + sintj - costk, 0 <= t <= (pi/2)

1. Evaluate the line integral F*dr.

2. Determine the arclength variable s from t.

3. Determine the unit tangent vector T(s).

4. Evaluate the total arclength L.

5. Write the line integral in the from F(x(s), y(s), z(s)) * T(s) ds explicitly from L to 0.

https://brainmass.com/math/vector-calculus/vector-fields-evaluating-integrals-29257

#### Solution Preview

See attachment

Let a vector field F be given by

F(x,y,z) = (x^3)i - (y^2)j + (2yz)k

and a curve C be given by

r(t) = 2ti + sintj - costk, 0 <= t <= (pi/2)

1. ...

#### Solution Summary

This shows how to evaluate line integral, determine arclength variable, and determine unit tangent vector.

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