Recently, I faced a problem to solve this integral

\(\int { xdy+ydx } \)

without any function \(y=f\left( x \right) \). A friend of mine helped me here. He told me to substitute \(xy=t\) so that \(xdy+ydx\) becomes \(dt\) and the integral gets evaluated to \(xy\)

Now I want to know more about this technique in calculus.

What this technique is known as?

Do we have a wiki about it here on Brilliant?

P.S.:I was totally awestruck when I solved this integral without knowing the function

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestThis is a simple Integration By parts question

\[\int{x dy} + \int{y dx} \\ \text{Integrating by parts we get} \\ x \int{dy} - \int{y dx} + \int {y dx} \\ = \boxed{xy} \]

Wiki

Log in to reply

nice!

Log in to reply

This is called

Solution by Inspection.You can find several such techniques in JEE-Advanced Books.Log in to reply

can you recommend one, please?

Log in to reply

Integral Calculus of Arihant Publication, that's a good one. It will help you master the whole integral calculus, but for that you will need to go through this book completely.

All the best !

Log in to reply

this question? I don't think the Gamma function is correct.

Sir, could you please look atLog in to reply

@Sandeep Bhardwaj Sir, please could you give me a link where I could buy the book? I couldn't find it on the Net.

Log in to reply

I'll do that when we do calculus in our coaching

Log in to reply

@Sandeep Bhardwaj sir, @Ishan Dasgupta Samarendra , @Azhaghu Roopesh M please help

Thanks!

Log in to reply

@Mayank Singh Sorry for responding late, I just came on Brilliant. On a slightly higher level, you could try Problems in Calculus of One Variable. The thing is that you will have to go through this carefully. But according to me, it's an excellent book. It even has Physics based applications as examples and questions.

Log in to reply

Thanks!

Log in to reply

Log in to reply

@Mayank Singh You could also try this site for the basics. Under the option 'Class Notes', look at Calculus II and III as well as Differential Equations.

Log in to reply

Log in to reply