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Remarks: Int(0->t): integral from 0 to t !

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- Thread starter yukcream
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Remarks: Int(0->t): integral from 0 to t !

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arildno

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Differentiate your equation to get your differential equation.

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arildno said:

Differentiate your equation to get your differential equation.

Yes I know I have to differential but if the diff. it with respect to t , what will happen to the second term on the left hand side?

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lurflurf

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Use the Leibniz Integral Rule.yukcream said:Yes I know I have to differential but if the diff. it with respect to t , what will happen to the second term on the left hand side?

[tex]\frac{d}{dt}\int_{a(t)}^{b(t)}f(x,t)dx=\int_{a(t)}^{b(t)}

\partial_tf(x,t)dx+f(x,t)\partial_tx|_{x=a(t)}^{x=b(t)}[/tex]

[tex]\frac{d}{dt}\int_{a(t)}^{b(t)}f(x,t)dx=\int_{a(t)}^{b(t)}

\frac{\partial}{\partial t}f(x,t)dx+f(x,t){\partial x}{\partial t}\right|_{x=a(t)}^{x=b(t)}[/tex]

http://mathworld.wolfram.com/LeibnizIntegralRule.html

for the initial condition you should know that

[tex]\int_0^0 f(x) dx=0[/tex]

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