How to integrate dv/dt = a

[Indranil]

[h=1]dv/dt = a, Here how to integrate dv and how to integrate a.dt? [x^(n+1) /n+1][/h]

 

[Deleted member 4993]

dv/dt = a, Here how to integrate dv and how to integrate a.dt? [x^(n+1) /n+1]

So you are given 'a' and you need to calculate 'x' - is that the question?

 

[Steven G]

dv/dt = a, Here how to integrate dv and how to integrate a.dt? [x^(n+1) /n+1]

Note that a is a constant. We know that all integrals have a constant and we will use v₀ for that constant. Why???

Int (a*dt) = at + v₀

 

[Dr.Peterson]

Note that a is a constant. We know that all integrals have a constant and we will use v₀ for that constant. Why???

Int (a*dt) = at²/2 + v₀

You didn't mean that, did you?

The real question here is, IS a a constant? If it is, then ∫dv = v + C₁, and ∫a dt = at + C₂.

 

[Steven G]

You didn't mean that, did you?

The real question here is, IS a a constant? If it is, then ∫dv = v + C₁, and ∫a dt = at + C₂.

No, I did not mean that and will edit it. I assumed (bad mistake, I know) that a is constant.
It is that if a is not a constant, then the integral could not be solved with the given information.

 

[Indranil]

You didn't mean that, did you?

The real question here is, IS a a constant? If it is, then ∫dv = v + C₁, and ∫a dt = at + C₂.

Yes 'a' is a constant (a = acceleration here)
But my question is how do you find 'v', integrating 'dv' and how you find 't', integrating 'dt'? Could you show me the steps, please?

 

[Deleted member 4993]

Yes 'a' is a constant (a = acceleration here)
But my question is how do you find 'v', integrating 'dv' and how you find 't', integrating 'dt'? Could you show me the steps, please?

Indranil, have you taken a formal course in calculus?

 

[Indranil]

Indranil, have you taken a formal course in calculus?

Not yet But here I am learning a great deal from basic to advance from the great teachers like you that's why I don't need to join any formal course and all of you teach here in an amazing way.

 

[Dr.Peterson]

Not yet But here I am learning a great deal from basic to advance from the great teachers like you that's why I don't need to join any formal course and all of you teach here in an amazing way.

No, we don't teach here. We tutor.

In order to learn calculus effectively, you must take an orderly course, not just ask random questions and get answers without context.

Now, you may "take" that course on your own, by reading a book or using an online course (of which there are many) without a teacher. If so, tutors can help. But it will be valuable if you can tell us what course/book you are using and where you are in the course. And if you are not doing anything like that, you really need to; that will take care of most questions before you ask them, because the material would be presented in an appropriate order.

In particular, you would have been taught, before seeing this problem, that ∫dv = v + C₁, and ∫a dt = at + C₂. These are just facts to know, and will be presented soon after defining the antiderivative.