Error in Thomas' Calculus 13th edition?

[Daniel McKinley]

Homework Statement

Section 11-2, Page 651, Example 3

Homework Equations

y = sin^3t and dy = 3cos^2t sint dt. Shouldn't there be a Minus Sign there?

The Attempt at a Solution

Answer is correct. But isn't there a missing Minus Sign?

 

[Chestermiller]

Homework Statement

Section 11-2, Page 651, Example 3

Homework Equations

y = sin^3t and dy = 3cos^2t sint dt. Shouldn't there be a Minus Sign there?

The Attempt at a Solution

Answer is correct. But isn't there a missing Minus Sign?

What makes you think that? Shouldn't it be $3sin^2tcostdt$?

 

[Stephen Tashi]

dy = 3cos^2t sint dt. Shouldn't there be a Minus Sign there?

Shouldn't that be "$3 \sin^2{t} \cos{t}\ dt$" ?

 

[Daniel McKinley]

The book has x-=cos^3 t and dx = 3 cos^2 t sin t dt That's where the minus sign appears to be missing.

 

[Stephen Tashi]

The book has x-=cos^3 t and dx = 3 cos^2 t sin t dt That's where the minus sign appears to be missing.

I don't understand the notation "x-=". You didn't say where the minus sign is missing.

 

[epenguin]

He doesn't fill in the missing steps? No they don't always, you are expected to do it yourself.

Best not to try and do this one in your head alone. Write it out and if you still have a problem ask again giving your work.

You're sure you copied the formulae exactly to us? As it stands, it looks like he has used some trigonometrical identitiy/ies which makes it not immediately obvious to most people.

 

[SammyS]

Homework Statement

Section 11-2, Page 651, Example 3

Homework Equations

y = sin^3t and dy = 3cos^2t sint dt. Shouldn't there be a Minus Sign there?

The Attempt at a Solution

Answer is correct. But isn't there a missing Minus Sign?

The book has x-=cos^3 t and dx = 3 cos^2 t sin t dt That's where the minus sign appears to be missing.

Hello Daniel McKinley. Welcome to PF !

It helps greatly to give us the entire problem (in this case an Example) as it was given in the textbook.

Here is a screen shot of what I could find for that example:

The author has done the problem correctly. As @epenguin has suggested, the author has skipped some steps.

Indeed, $\ dx = -3\cos^2 t \sin t \,dt\$ with a negative sign.

If you consider the limits of integration, the negative sign has the effect of switching the limits of integration, giving the integral you see above.

 

[Daniel McKinley]

Thank you SammyS!