Hi, My textbook says the integral is: . The part I'm not sure about is how they can put out of the integral sign, and just integrate , as is a function of time. Thanks.
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Originally Posted by algorithm Hi, My textbook says the integral is: . The part I'm not sure about is how they can put out of the integral sign, and just integrate , as is a function of time. Thanks. My guess is that they are not. With a little abuse of notation multiply both sides of the equation by Now integrate both sides to get
y dy/dt = (1/2) d(y²)/dt x dx/dt = (1/2) d(x²)/dt y dy/dt = x dx/dt hence d(y²)/dt = d(x²)/dt Since the derivatives are equal, the functions differ only from a constant; y²-x² = c
I see. Thanks for your explanations.
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