Is there any application of indefinite integration in engineering?

Question

i want to know the practical applications of indefinite integrals.

Answer 1

It is not common, but a general engineering problem may be set up with an indefintie integral that can be solved in closed form, therefore providing an equation that gives the nature of the solution without exact numbers.

A simple example to show how it might be done: if you have a voltage feeding a capacitor through a resistor, the capacitor's voltage is given by C*dVc/dt=i; I=(Vs-Vc)/R. dV/dt = (Vs-Vc)/RC,

dVc/(Vs_vc) = dt/RC

now we integrate both sides with an indefinite integral, getting

-ln(Vs-Vc) + K = t/RC where K is a constant to be determined.

This can be written ln(Vs-Vc)=K-t/RC, which is the same as

Vs-Vc = e^(K-t/RC)

Vs-Vc = e^K * e^(t/RC); now let e^K equal a new constant K'.

Vs-Vc = K'e^(t/RC)

Vc = Vs - K'e^(t/RC)

Now we know from the properties of a capacitor that the voltage cannot change instantly, and we set the initial condition across the capacitor at t=0 that Vc = 0. This means that Vc(0) = Vs - K' = 0. or K' = Vs. Finally we get an equation for the voltage across the capacitor

Vc= Vs - Vse^-t/RC, or Vc = Vs(1-e^-t/RC)

which gives us the way the capacitor will respond generally.

Answer 2

I can't think of an example for an "indefinite integral". Most differential equations and other applications requiring integration are done over a definite range, related to the specific problem in question.

Answer 3

indefinite integration can be applied to space related prolems. indefinite integration dont have limits.so they are used in space research where assumptions play a major part.

Answer 4

Yes, many physical systems are represented by differential equations. These can only be solved by a thorough knowledge of integration.

Answer 5

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