I Determining the limits of x

1. Dec 11, 2016

King_Silver

I am currently practicing questions on Green's Theorem however in some questions I have been given a finite region enclosed between a parabola and a horizontal line.

In these questions I am given 2 values of y but none of x.
In one question I was given that y = x^2 and y = 9 and was immediately able to spot that x satisfies this for the values -3 and 3 therefore x [-3,3] and y [ x^2, 9]

However I now have come across a situation where y = 3x^2 and y = 5 and I cannot seem to spot any sort of relationship between these 2. Based on previous questions I figured these values of x would satisfy both values of y given.

Can anybody tell me how these limits are established? I've integrated in terms of y and now have all x terms but do not know what limits to apply to the integral.

2. Dec 11, 2016

eys_physics

You can do in exactly the same way:
$$y=3x^2$$, divide by 3 on both sides to get
$$y/3=x^2$$, and use the same method as for $y=x^2$. I would also recommend a figure, in order to see more clearly the region.

3. Dec 11, 2016

Staff: Mentor

What does "y [x^2, 9]" mean?
It would be much simpler and clearer to say that if x = 3 or x = -3, then y = 9.
It seems odd to me that you are working with Green's Theorem, but are having trouble solving very elementary equations such as $3x^2 = 5$. Some time spent reviewing elementary algebra would be very beneficial.

4. Dec 11, 2016

King_Silver

Sorry that should have said the limits of y are x^2 and 9 so when we integrate with respect to y those are the limits. It was a poorly written post.

That is embarrassing, I totally overlooked the other value of y despite specifying it. Brain fart. Thanks for the help!