Evaluate the integral by interpreting it in terms of areas.

[Hemolymph]

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]

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.

Where did the rectangle come from? It's just a semicircular area.

 

[Hemolymph]

Where did the rectangle come from? It's just a semicircular area.

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
I guess i tried to apply the same technique to this problem.
The answer came out to be 5+(25pi)/4

 

[haruspex]

I was doing a simliar problem of [-5,0] where it was evaluating 1+rad(25-x^2) dx

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?

 

[Mark44]

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

When you're using what you found in a "similar" problem, make sure it's actually similar to the one you're working on.

As suggested by others in this thread, a quick sketch of the graph of x² + y² = 4 would show that your region is just the upper half of a circle.

Sketching a graph is usually the first thing you need to do in these problems.

I guess i tried to apply the same technique to this problem.
The answer came out to be 5+(25pi)/4

 

[Hemolymph]

Thanks for the advice/ help