- #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?
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)?
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.
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.
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.
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.
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.