Help with an integral that has differentials inside of it

In summary, an integral with differentials inside of it is a mathematical concept that represents the inverse operation of differentiation and is used to find the area under a curve or the total value of a function over a given interval. To solve this type of integral, one must use integration techniques such as substitution, integration by parts, or partial fractions, and apply the fundamental theorem of calculus. Understanding integrals with differentials inside of it is important in various fields of science and engineering, and common mistakes include forgetting the constant of integration and using incorrect techniques or limits. To improve skills in solving these integrals, one can practice with examples and problems and review fundamental rules and techniques.
  • #1
enerj
3
0
So my calculus isn't as sharp as I'd like it, and I am having trouble solving this diff eq, and I know the correct method is double integration. I also know the general solution to be

T(r) = A*ln(r) + B , A and B are constants

Thanks in advance
 

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  • #2
What have you done so far?
 

1. What is an integral that has differentials inside of it?

An integral with differentials inside of it is known as an integral with respect to a variable. It is a mathematical concept that represents the inverse operation of differentiation and is used to find the area under a curve or the total value of a function over a given interval.

2. How do I solve an integral with differentials inside of it?

To solve an integral with differentials inside of it, you will need to use integration techniques such as substitution, integration by parts, or partial fractions. You will also need to apply the fundamental theorem of calculus, which states that the integral of a function is equal to the difference between its antiderivative evaluated at the upper and lower limits of integration.

3. Why is it important to understand integrals with differentials inside of it?

Understanding integrals with differentials inside of it is crucial in many fields of science and engineering, including physics, economics, and statistics. These integrals are used to solve real-world problems and make predictions based on data. They also serve as the basis for more advanced concepts such as multivariable calculus and differential equations.

4. What are some common mistakes when working with integrals with differentials inside of it?

One common mistake when working with integrals with differentials inside of it is forgetting to include the constant of integration. Another mistake is using the incorrect substitution or integration technique. It is also important to be careful with the limits of integration and to pay attention to the sign of the function being integrated.

5. How can I practice and improve my skills in solving integrals with differentials inside of it?

The best way to practice and improve your skills in solving integrals with differentials inside of it is by working through various examples and problems. You can find practice problems in textbooks, online resources, or through a tutor or study group. It is also helpful to understand the underlying concepts and to review the fundamental rules and techniques for integration.

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