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zeromaxxx
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Homework Statement
Integral of (k/x)-1/2
Homework Equations
The Attempt at a Solution
2(k/x)1/2
How do I find the integral of the inner function (k/x)?
The integral of (k/x)-1/2 is 2k√x + C, where C is a constant.
To solve for the integral of (k/x)-1/2, you can use the Power Rule for Integrals, which states that the integral of x^n is (x^(n+1))/(n+1) + C. In this case, n = -1/2, so the integral becomes (k/x)^(1/2) + C. Then, using the Constant Multiple Rule for Integrals, the final answer is 2k√x + C.
The Step-by-Step Guide is designed to help you understand and follow the process of solving the integral of (k/x)-1/2. It breaks down each step and provides explanations and examples, making it easier for you to solve similar integrals in the future.
Yes, you can solve this integral without the Step-by-Step Guide. However, the guide can be a helpful tool in understanding the process and avoiding mistakes. It also provides alternative methods and tips for solving integrals.
Yes, there are some special cases and exceptions when solving this integral. For example, if the value of k is 0, the integral becomes ∫(0/x)-1/2 dx, which is undefined. Additionally, if the value of x is negative, the integral becomes ∫(k/-x)-1/2 dx, which can be solved using trigonometric substitutions. It is important to check for these special cases when solving integrals.