# Converting derivative into integral

• zealous131
In summary, the person is asking for help in converting an equation from differential form to integral form in Calculus. They clarify that Q is only a function of time and does not involve B, making the process easier. They thank JJacquelin for providing a solution and appreciate Chiro's advice for future reference.
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!

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zealous131 said:
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).

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!

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.

## What is the process of converting a derivative into an integral?

The process of converting a derivative into an integral is known as integration. This involves finding the original function from its derivative by reversing the rules of differentiation.

## Why is it important to be able to convert derivatives into integrals?

Converting derivatives into integrals is important because it allows us to find the original function from its derivative, which is useful in many applications such as finding areas under curves, solving differential equations, and calculating total change.

## What are the different methods for converting derivatives into integrals?

There are several methods for converting derivatives into integrals, including the power rule, substitution, integration by parts, and partial fractions. Each method is useful for different types of functions and can be applied depending on the given problem.

## How do I know which method to use when converting a derivative into an integral?

The method to use when converting a derivative into an integral depends on the type of function and the given problem. It is important to have a good understanding of each method and how it applies to different types of functions in order to choose the most appropriate one.

## What are some tips for solving problems involving converting derivatives into integrals?

Some tips for solving problems involving converting derivatives into integrals include: being familiar with the different methods, practicing regularly, carefully reading the given problem to determine the appropriate method to use, and checking your answer using differentiation to ensure it is correct.

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