The discussion revolves around evaluating the integral of the function defined by the equation \( y = \sqrt{4 - x^2} \) over the interval from -2 to 2. Participants identify the geometric interpretation of the integral in terms of areas, specifically relating to a semicircle.
The conversation is ongoing, with participants providing insights and questioning the assumptions made in the original poster's approach. Suggestions to sketch the graph have been made to clarify the area being evaluated, indicating a productive direction in the discussion.
Participants note that the original problem may have been misinterpreted by trying to apply techniques from a different problem that involved a rectangle. There is an emphasis on ensuring the similarity of problems before applying previous methods.
Hemolymph said:Homework Statement
from [-2,2] rad(4-x^2)
Homework Equations
The Attempt at a Solution
I know its a circle and i get the equation to be y^2+x^2=4
and I believe it has to be divided into a circle and rectangle
so the area of the rectangle i got to be 2
the circle i got to be 1/2(since its a half circle) times ∏(2)^2
the answer i got is
2+2pi (which is wrong) don't know where I went wrong tho.
Curious3141 said:Where did the rectangle come from? It's just a semicircular area.
The 1+ gave the rectangle there. You have no corresponding term here. Did you sketch the curve? Do you see a rectangle when you do?Hemolymph said:I was doing a simliar problem of [-5,0] where it was evaluating 1+rad(25-x^2) dx
When you're using what you found in a "similar" problem, make sure it's actually similar to the one you're working on.Hemolymph said:I was doing a simliar problem of [-5,0] where it was evaluating 1+rad(25-x^2) dx
And the solution had a the area broken up into a rectangle and a semicircle
Hemolymph said:I guess i tried to apply the same technique to this problem.
The answer came out to be 5+(25pi)/4