Converting derivative into integral

[zealous131]

Hi,

I need to ask a very basic question and am very weak at calculus. I have an equation d(B)/dt=Q/K. Where K is a constant and Q is a function of time. B is the variable, which when differentiated w.r.t. time gives the Q. I want to convert this equation into integral form. Can anyone help me out on this? I will really really appreciate any help! Thanks!

 

[JJacquelin]

hoping this will help you :

 

[chiro]

Hi,

I need to ask a very basic question and am very weak at calculus. I have an equation d(B)/dt=Q/K. Where K is a constant and Q is a function of time. B is the variable, which when differentiated w.r.t. time gives the Q. I want to convert this equation into integral form. Can anyone help me out on this? I will really really appreciate any help! Thanks!

Hey zealous131 and welcome to the forums.

Does Q only involve time (t) or does it also involve B? If the answer is no then JJacquelin has provided a very good outline of what to do. If not, then you will need to state how B is involved in with Q. If you don't understand what I'm saying and you've only been told that Q is a function of t (i.e. Q(t)) then don't worry about my advice (but keep it in mind later on if you have to solve things like this).

 

[zealous131]

Thanks a lot JJacquelin for providing me the solution. I really apreciate it! Thanks Chiro for your valuable comment, Q is only a function of time and doesn't depend on B so that makes ife easier. I will definitely keep the point you've mantioned. Thanks!

 

[blue_raver22]

Sure, I can help with converting this equation into integral form. First, let's start with the definition of a derivative. A derivative is the rate of change of a function with respect to a variable. In this case, the derivative of B with respect to time (dt) is equal to the function Q divided by the constant K.

To convert this into integral form, we need to use the fundamental theorem of calculus. This states that the integral of a derivative is equal to the original function. In this case, the integral of d(B)/dt is equal to B, the original function.

Using this information, we can rewrite the equation as:

∫ d(B)/dt dt = ∫ Q/K dt

Now, we can simply integrate both sides with respect to time:

B = ∫ Q/K dt

This is the integral form of the original equation. It represents the total accumulation of the function Q over time. I hope this helps! Let me know if you have any further questions.