You are Here: Home >< Maths

# Differentiating under the integral sign watch

1. I've searched for this on the Internet, and I'm struggling to understand it. Most explanations are referring to partial derivatives or multivariable functions.

Does the method use the result ?

So, for an example, would it be possible to find this way? (And if so, how?)
2. (Original post by Glutamic Acid)
I've searched for this on the Internet, and I'm struggling to understand it. Most explanations are referring to partial derivatives or multivariable functions.

Does the method use the result ?
Not in general, although you might use that as well.

The idea of differentiating under the integral sign is that under suitable circumstances,

e.g. .

So the rule above gives

That is, .

Strictly speaking, the differentiation w.r.t. a is a partial derivative.

So, for an example, would it be possible to find this way? (And if so, how?)
It is possible, but it isn't easy, and it's very unobvious.

See Q14 on http://www.damtp.cam.ac.uk/user/examples/A3a.pdf
3. (Original post by yusufu)
I don't quite follow; there are three.
4. (Original post by Glutamic Acid)
I don't quite follow; there are three.
5. (Original post by DFranklin)
Not in general, although you might use that as well.

The idea of differentiating under the integral sign is that under suitable circumstances,

e.g. .

So the rule above gives

That is, .

Strictly speaking, the differentiation w.r.t. a is a partial derivative.
Thanks, I think I get it, it was the step of putting d/da inside the integral which I was missing.

So, just to check:
.

.

.

But this seems to break down even when a = 1. Or is this a case where differentiating under the integral won't work?
It is possible, but it isn't easy, and it's very unobvious.

See Q14 on http://www.damtp.cam.ac.uk/user/examples/A3a.pdf
I see. There's no way I'd have thought of it, and I doubt I can prove it anyway.
6. d/da cos(ax) = -x sin(ax), surely?
7. Oh, haha, silly mistake. Thanks.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 12, 2008
Today on TSR

Will it ever be possible?

### University open days

1. University of Cambridge
Wed, 26 Sep '18
2. Norwich University of the Arts
Fri, 28 Sep '18
3. Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 29 Sep '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE