Discover the Integral of (k/x)-1/2 | Solve with Our Step-by-Step Guide

  • Thread starter zeromaxxx
  • Start date
  • Tags
    Integral
In summary, the integral of (k/x)-1/2 is 2k√x + C, where C is a constant. To solve for the integral, you can use the Power Rule for Integrals and the Constant Multiple Rule for Integrals. The Step-by-Step Guide is designed to help you understand and follow the process of solving this integral, but it is not necessary. There are special cases and exceptions to consider when solving this integral, such as when k or x have specific values.
  • #1
zeromaxxx
17
0

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)?
 
Physics news on Phys.org
  • #2
K is a constant, i presume. Put (1/x)^(-1/2) under the classical form x^a. Find a then apply the rules for integrating x^a you (probably) learned in class.
 

What is the integral of (k/x)-1/2?

The integral of (k/x)-1/2 is 2k√x + C, where C is a constant.

How do I solve for the integral of (k/x)-1/2?

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.

What is the purpose of the Step-by-Step Guide for solving this integral?

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.

Can I solve this integral without the Step-by-Step Guide?

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.

Are there any special cases or exceptions when solving this integral?

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.

Similar threads

  • Calculus and Beyond Homework Help
Replies
7
Views
641
  • Calculus and Beyond Homework Help
Replies
5
Views
222
  • Calculus and Beyond Homework Help
Replies
1
Views
383
  • Calculus and Beyond Homework Help
Replies
2
Views
857
  • Calculus and Beyond Homework Help
Replies
8
Views
116
  • Calculus and Beyond Homework Help
Replies
4
Views
893
  • Calculus and Beyond Homework Help
Replies
3
Views
685
  • Calculus and Beyond Homework Help
Replies
8
Views
709
  • Calculus and Beyond Homework Help
Replies
7
Views
641
Replies
1
Views
875
Back
Top