Define a constant a

[TeaAndCrackers]

Blue curve: y=x^2
Black line: y=4
Red line: y=a

''The area which is limited by y=x^2, y=4 and y=a is equal to the area limited by y=x^2 and y=a. Define the constant a.''

This exercise was supposed to be solved with integrals.
I've calculated the area between y=x^2 and y=a by integrating, but I don't know how to continue. Could someone help?

 

[MarkFL]

Hello, and welcome to FMH!

I would use the even symmetry and write:

[MATH]\int_0^a y^{\frac{1}{2}}\,dy=\int_a^4 y^{\frac{1}{2}}\,dy[/MATH]
Now, we can solve for \(a\)...can you proceed?

 

[TeaAndCrackers]

Thank you for replying! This helped me. I'm still a bit confused though, where does the y^1/2 come from?

 

[Dr.Peterson]

Thank you for replying! This helped me. I'm still a bit confused though, where does the y^1/2 come from?

Solve y = x^2 for x.

That's what you have to do in order to integrate with respect to y rather than x.

Alternatively, you could find the area of the bottom part (y=0 to a) and of the whole (y=0 to 4), by integrating with respect to x, and think about how those two areas have to be related.