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Question Number 8734 by tawakalitu last updated on 24/Oct/16

$$\mathrm{Evaluate}\mathrm{the}\mathrm{integral}$$$$\int [\mathrm{a}(\stackrel{\bullet }{\mathrm{b}}.\mathrm{a}+\mathrm{b}.\stackrel{\bullet }{\mathrm{a}})+\stackrel{\bullet }{\mathrm{a}}(\mathrm{b}.\mathrm{a})-2(\stackrel{\bullet }{\mathrm{a}}.\mathrm{a})\mathrm{b}-\stackrel{\bullet }{\mathrm{b}}\mid \mathrm{a}{\mid }^2]\mathrm{dt}$$$$\mathrm{In}\mathrm{which}\stackrel{\bullet }{\mathrm{a}},\stackrel{\bullet }{\mathrm{b}}\mathrm{are}\mathrm{the}\mathrm{derivatives}\mathrm{of}\mathrm{a},\mathrm{b}\mathrm{with}$$$$\mathrm{respect}\mathrm{to}\mathrm{t}$$

Commented by Yozzias last updated on 24/Oct/16

$$\int (\mathrm{a}\frac{\mathrm{d}}{\mathrm{dt}}(\mathrm{a}.\mathrm{b})-\stackrel{\bullet }{\mathrm{a}}(\mathrm{a}.\mathrm{b})-\stackrel{\bullet }{\mathrm{b}}\left({\mathrm{a}}^2\right))\mathrm{dt}$$$$\int (\mathrm{a}\frac{\mathrm{d}}{\mathrm{dt}}(\mathrm{a}.\mathrm{b})-\mathrm{a}\{\stackrel{\bullet }{\mathrm{a}}\left(\mathrm{b}\right)+\stackrel{\bullet }{\mathrm{b}}\left(\mathrm{a}\right)\})\mathrm{dt}$$$$=\int (\mathrm{a}\frac{\mathrm{d}}{\mathrm{dt}}(\mathrm{a}.\mathrm{b})-\mathrm{a}\frac{\mathrm{d}}{\mathrm{dt}}(\mathrm{a}.\mathrm{b}))\mathrm{dt}$$$$=\mathrm{c}$$

Commented by tawakalitu last updated on 25/Oct/16

$$\mathrm{Thank}\mathrm{you}\mathrm{sir}.$$

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