Compute the vector valued integral

We compute,

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Stumbling Robot

A Fraction of a Dot
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Category: Exercises

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Compute the vector valued integral

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Compute the integral of *(sin t, cos t, tan t)*

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Compute the integral of *(t, t*^{1/2}, e^{t})

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Prove that the angle between *F(t)* and *F'(t)* is constant for a given vector function

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Compute derivatives of *F(t) = log (1+t*^{2}) **i** + arctan t **j** + 1/(1+t^{2}) **k**

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Compute derivatives of *F(t) = cosh t ***i** + sinh (2t) **j** + e^{-3t}**k**

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Compute derivatives of *F(t) = 2e*^{t}**i** + 3e^{t}**j**

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Compute derivatives of *F(t) = (arcsin t, arccos t)*

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Compute derivatives of *F(t) = (cos t, sin*^{2} t, sin (2t), tan t)

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Compute the first two derivatives of *F(t) = (t, t*^{2}, t^{3}, t^{4})

Exercises and solutions from textbooks

Compute the vector valued integral

We compute,

Compute the vector-valued integral

We compute

Compute the vector-valued integral

We compute,

Consider the vector-valued function

Prove that the angle between and is a constant.

*Proof.* First, we have

Thus,

Hence, and are orthogonal, so the angle between them is constant,

Compute the derivatives and of the vector valued function

We compute

Compute the derivatives and of the vector valued function

We compute

Compute the derivatives and of the vector valued function

We compute,

Compute the derivatives and where is the vector valued function

We compute

Compute the derivatives and of the vector valued function

We compute

Compute the derivatives and of the vector valued function

We compute,