C4 Changing limits in integration

My maths terminology is horrible, so I'd be better off pointing to this video.

https://www.youtube.com/watch?v=TGb2oj4ue-4#t=141

Why is it that when changing the limits (2:21) in video, he doesn't consider the negative roots in the equation?

Reply 1

Notnek

21

Original post by scientific222

My maths terminology is horrible, so I'd be better off pointing to this video.

https://www.youtube.com/watch?v=TGb2oj4ue-4#t=141

Why is it that when changing the limits (2:21) in video, he doesn't consider the negative roots in the equation?

The negative root is not of interest here since the denominator contains the positive root.

If the fraction was

\displaystyle \frac{1}{4-\sqrt{x-1}}

then you could also write this as

\displaystyle \frac{1}{u}

.

He's not solving the equation

\displaystyle (u-4)^2=x-1

but instead showing that

\displaystyle u=4+\sqrt{x-1}

satisfies

\displaystyle (u-4)^2=x-1

.

(edited 9 years ago)

Reply 2

TenOfThem

18

Original post by scientific222

My maths terminology is horrible, so I'd be better off pointing to this video.

https://www.youtube.com/watch?v=TGb2oj4ue-4#t=141

Why is it that when changing the limits (2:21) in video, he doesn't consider the negative roots in the equation?

Effectively he is using the substitution

u=4+\sqrt{x-1}

but it was given differently to start with

Remember - in substitution we choose what to substitute

C4 Changing limits in integration

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