Question about integration (1 Viewer)

[pikachu975]

http://prntscr.com/fs8e38 - question

http://prntscr.com/fs8dxe - answer

Since they didn't give a domain for theta, should the answer be plus or minus x/9sqrt(9-x^2) + C ?

Thanks

 

[si2136]

http://prntscr.com/fs8e38 - question

http://prntscr.com/fs8dxe - answer

Since they didn't give a domain for theta, should the answer be plus or minus x/9sqrt(9-x^2) + C ?

Thanks

It should just be positive. What do you mean by domain, you assume that the angle is acute when you want to draw the triangle.

EDIT: If you're talking about Pythagorean, distance is always positive.

 

[pikachu975]

It should just be positive. What do you mean by domain, you assume that the angle is acute when you want to draw the triangle.

EDIT: If you're talking about Pythagorean, distance is always positive.

They give x = 3sintheta, so we don't know if it's the first or second quadrant so if it's the second quadrant then tantheta is negative, so just wondering if it would be plus or minus.

EDIT: http://prntscr.com/fs8ru9

From this question they drew a triangle with plus or minus which is where I got the idea from

 

[si2136]

They give x = 3sintheta, so we don't know if it's the first or second quadrant so if it's the second quadrant then tantheta is negative, so just wondering if it would be plus or minus.

EDIT: http://prntscr.com/fs8ru9

From this question they drew a triangle with plus or minus which is where I got the idea from

I just always assumed it was positive, I never got an integration q where the answer was plus minus

 

[pikachu975]

Funny Hahah just did this question in a CSSA paper.

Getting from the second last step to the last step you must construct a triangle and hence your theeta is less than 90. This automatically puts it in the first quadrant and hence your answer is always positive.

What about the screenshot of the answers in another question in my previous post around 3 posts higher?

 

[Blast1]

http://prntscr.com/fs8e38 - question

http://prntscr.com/fs8dxe - answer

Since they didn't give a domain for theta, should the answer be plus or minus x/9sqrt(9-x^2) + C ?

Thanks

As a quick way of showing why the antiderivative cannot be minus x/(9sqrt(9-x^2)) + C, try differentiating this expression and see if you get the original expression in the question.
The answer for this question is plus x/(9sqrt(9-x^2)) + C because they assumed that costheta = plus sqrt (1-sin^2 theta) when moving from line 1 to 2, and implicitly assumed this again when moving from line 4 to 5. If they assumed that cos theta = minus sqrt(1-sin^2theta), then the minuses would've cancelled out since they use this assumption in moving from line 1 to 2, then again from line 4 to 5. So in the end, your final expression for the antiderivative would be the plus version.