How to integrate this to solve for Q?

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In summary, the variable to solve for when integrating can be identified by looking at the integrand, and the process involves finding the antiderivative of the function. The integration technique to use depends on the form of the integrand, and it is possible to solve for Q using numerical methods. To check if your integration is correct, you can take the derivative of your solution or use online tools or graphing software.
  • #1
Math10
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Homework Statement


How to solve for Q in dQ/dt=2-0.1Q?

Homework Equations


None.

The Attempt at a Solution


dQ/(2-0.1Q)=dt
Now what?
 
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  • #2
Now integrate both sides and solve for Q.
 
  • #3
I got t+C after integrating the right side but I don't know how to integrate the left side, is it ln abs(2-0.1Q)?
 
  • #4
Math10 said:
I got t+C after integrating the right side but I don't know how to integrate the left side, is it ln abs(2-0.1Q)?

Close but not quite. Write out your u substitution for that integral.
 

1. How do I identify the variable to solve for when integrating?

The variable to solve for when integrating can be identified by looking at the integrand, or the expression being integrated. The variable that appears in the integrand will be the variable to solve for.

2. What is the process for integrating a function?

The process for integrating a function involves finding the antiderivative of the function, or the function that when differentiated will give the original function. This is done by using integration techniques such as u-substitution, integration by parts, or trigonometric substitution.

3. How do I know which integration technique to use?

The integration technique to use depends on the form of the integrand. For example, if the integrand contains a polynomial, the integration technique of choice may be u-substitution. If the integrand contains a product of two functions, integration by parts may be used. It is important to practice and become familiar with different integration techniques in order to determine the best approach for a given integrand.

4. Can I solve for Q using numerical methods instead of integration?

Yes, it is possible to solve for Q using numerical methods such as the trapezoidal rule or Simpson's rule. These methods involve approximating the area under the curve of the function being integrated. However, integration by hand is often preferred as it provides an exact solution.

5. How can I check if my integration is correct?

To check if your integration is correct, you can take the derivative of your solution and see if it matches the original function. Additionally, you can use online integration calculators or graphing software to verify the area under the curve of your solution. It is also helpful to practice and check your work with different examples.

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