- #1

wizard85

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## Homework Statement

If [tex]{\vec{V}(t)[/tex] is a vector function of [tex] t [/tex], find the indefinite integral:

[tex] \int (\vec{V}\times \frac{d^2\vec{V}}{dt^2}) \,dt [/tex]

## Homework Equations

## The Attempt at a Solution

I have solved it by decomposing and integrating each terms of vector [tex]\vec{V}\times \frac{d^2t}{dt^2}[/tex], so I have:

[tex]

\vec{V}\times \frac{d^2\vec{V}}{dt^2}= \hat i (V_y * \frac{d^2V_z}{dt^2} - V_z * \frac{d^2V_y}{dt^2}) - \hat j (V_x * \frac{d^2V_z}{dt^2} - V_z * \frac{d^2V_x}{dt^2}) + \hat k (V_x * \frac{d^2V_y}{dt^2} - V_y * \frac{d^2V_x}{dt^2})

[/tex]

and the integral will be:

[tex]

\int (\vec{V}\times \frac{d^2\vec{V}}{dt^2}) \,dt = \hat i (\int (V_y * \frac{d^2V_z}{dt^2})\,dt - \int (V_z * \frac{d^2V_y}{dt^2})\,dt) - \hat j (\int (V_x * \frac{d^2V_z}{dt^2})\,dt - \int (V_z * \frac{d^2V_x}{dt^2}))\,dt + \hat k (\int (V_x * \frac{d^2V_y}{dt^2})\,dt - \int (V_y * \frac{d^2V_x}{dt^2}),dt)

[/tex]where [tex]\hat i[/tex],[tex]\hat j[/tex] and [tex]\hat k[/tex] are the three unit vectors with respect to frame of reference [tex](x,y,z)[/tex]My questions is: that's the right way or there exist some other way to resolve it in a more faster manner?

Thanks to all who will answer me ;)

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