Hard Integration by Substitution Question

[Skelly4444]

I have attached my workings for this difficult integration question together with a printout from an online integral calculator.

My question to the forum is that when we use the substitution x=3sin(u) why is the online integral calculator not acknowledging the negative sign in front of the 3cos(u)

Surely if you differentiate x=3sin(u) then dx/du would be -3cos(u) ??

I have been replacing dx with -3cos(u)du but the online integral calculator doesn't include the negative sign and so our answers differ?

Any ideas would be appreciated.

 

[Steven G]

Surely if you differentiate x=3sin(u) then dx/du would be -3cos(u) ?? Not true
(sinx)' = cosx
(cosx)' = -sinx

 

[BigBeachBanana]

Hi Skelly4444,
I've been doing you a favour by opening the pdf and posting the image of your pdf. Not everyone here is willing to open a pdf because of the potential virus. In the future, please attach an image instead.

 

[Skelly4444]

Sorry about that, I wasn't aware that PDFs were risky.
I had my derivatives and integrals chart in front of me when I was tackling this question and foolishly looked at the wrong chart when differentiating.
What a silly billy I am!
Thanks anyway.

 

[topsquark]

Sorry about that, I wasn't aware that PDFs were risky.
I had my derivatives and integrals chart in front of me when I was tackling this question and foolishly looked at the wrong chart when differentiating.
What a silly billy I am!
Thanks anyway.

Better to ask then to remain ignorant!

-Dan

 

[Steven G]

Good PDFs are not risky to open. However, some bad people put viruses in their PDF which obviously is not good. Hence, it is risky opening up a PDF since it might come from someone who put a virus in it.