Question

Please solve it ....

Answer 1

Hi there...

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This 1 is quite easy...

Just integrate....

c...

A is a vector and d²/dt²(A) is the second order derivative of vector A wrt t....

and all of us know already that $\int\ {dA/dt} \, dt =A$

now as vector A is differentiated with respect to t we can say A has certain parameters which change with t...

now as we know A is dependent on t we can differentiate this only by using the  formula

$\int\ {f.g} \, dx = f\int\ {g} \, dx -\int\ ({d/dx(f)\int\ {g} \, dx} \, )dx$

⇒

$\int\ {<strong>A </strong>. d²/dt²(<strong>A</strong>)} \, dt = <strong>A . </strong>d/dt(<strong>A)</strong> -\int\  {<strong> </strong>(d/dt(<strong>A)</strong>)²}dx$

= A . d/dt(A) -\int\  { (d/dt(A))²}dx