If y = √ 4 - x^2 then the area of the region limited by this curve y and the x axis is

a) ¶

b) 2¶

Calculate the correct result.

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- August 3rd 2006, 10:09 AMbret80Area between curve and x axis
If y = √ 4 - x^2 then the area of the region limited by this curve y and the x axis is

a) ¶

b) 2¶

Calculate the correct result. - August 3rd 2006, 10:10 AMThePerfectHackerQuote:

Originally Posted by**bret80**

A semi-circle with radius 2.

Instead of finding the complicated,

Simplfy, use the formula from geometry.

The area of the circle is,

Since this is half the answer is,

- August 3rd 2006, 01:08 PMSoroban
Hello, bret80!

Quote:

If , then the area of the region limited by and the x-axis is

Calculate the correct result.

If you are expected to do this with*Calculus*,

. . you need to know Trig Substitution (and a bit of Trig).

I'll baby-step through it for you . . .

Let

. . and

Substitute: .

Double-angle identity: .

We have: .

Then: .******

. .

. .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

******

A change of limits . . .

Since

. . . .