binbagsss said:Homework Statement
How to integrate
## \frac{dx}{dt}=\sqrt{\frac{k}{x}-1}##
AND
## \frac{dx}{dt}=\sqrt{\frac{k}{x}+1}##
k a constant here.
I'm unsure what substitution to do.
Many thanks in advance.
Homework Equations
The Attempt at a Solution
I can't really get started as I'm unsure what substition is needed.
I think a trig but don't know what?many thanks in advance.
Fred Wright said:Try expressing your integrals in a form that can be found in a table of integrals. It took me two minutes to find the answer to your question. If you are supposed to derive your answer from first principles, at least you will have something to work towards.
A good start would be to write as an integral, in as simple a form as you can, instead of leaving it as a differential equation.binbagsss said:I can't really get started
An integration question involving square root is a type of mathematical problem that requires finding the antiderivative of a function containing a square root. This is also known as solving for the integral of a square root function.
To solve an integration question involving square root, you can use techniques such as substitution, integration by parts, or trigonometric substitution. It is important to understand the properties and rules of integration in order to successfully solve these types of questions.
Some common mistakes when solving an integration question involving square root include forgetting to include the constant of integration, making errors in the substitution process, and not simplifying the answer. It is important to carefully check your work and double check your steps to avoid these mistakes.
While some calculators may have the capability to solve integration problems, it is important to understand the steps and concepts behind solving these types of questions. Using a calculator alone may not help you fully understand the solution process.
Integration questions involving square root are important because they are used in various fields of science and engineering, such as physics, chemistry, and economics. They also help in understanding and solving more complex integration problems.