I came across this integral of a vector valued function.(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int \mathbf A(t) \vec{w(t)} dt = \int \mathbf B(t) [/tex].

I want to isolate [itex] \vec{w(t)} [/itex] and so I multiply by [itex] \left (\int \mathbf A(t) dt \right)^{-1} [/itex] on both sides.

[tex] \left (\int \mathbf A(t) dt \right)^{-1} \int \mathbf A(t) \vec{w(t)} dt = \left (\int \mathbf A(t) dt\right)^{-1} \int \mathbf B(t) dt [/tex]

I thought the correct form would be

[tex] \int \vec{w(t)} dt = \left (\int \mathbf A(t) dt\right)^{-1} \int \mathbf B(t) dt [/tex].

But it turns out I get the right answer if I take

[tex] \vec{w(t)} = \left (\int \mathbf A(t) dt \right)^{-1} \int \mathbf B(t) dt [/tex].

Can anyone show why the second form is correct?

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# Integral of a vector valued function

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