Posted by **mikayla** on Wednesday, April 18, 2007 at 9:06pm.

find the area between the x-axis and the graph of hte given function over the given interval:

y = sqrt(9-x^2) over [-3,3]

you need to do integration from -3 to 3.

First you find the anti-derivative

when you find the anti-derivative you plug in -3 to the anti-derivative and then plug in 3 and find the difference of : f(-3)-f(3). Hope this helps :)

but how to you find the antideriv?

Paste sqrt(9-x^2) into

http://integrals.wolfram.com/index.jsp
This is an arcsin derivative.

Substitute x = 3 sin(t). Then t goes from - pi/2 to pi/2.

sqrt[9 - x^2] = 3 sqrt[1 - sin^2(t)] =

3 |cos(t)|

and dx = 3 cos(t) dt

So, you have to integrate 9 cos^2(t) from t = -pi/2 to pi/2 (note that in the interval cos(t) is positive so you can remoce the absolute value signs).

Since we are integrating over an entire period of the cos^2 the integral would be the same if you replace cos^2 by sin^2. By replacing cos^2 by cos^2 + sin^2 you thus obtain twice the value of the integral but since sin^2 + cos^2 = 1 that's 9 pi. So, the integral is 9/2 pi.

## Answer This Question

## Related Questions

- math - find the area between the x-axis and the graph of hte given function over...
- cal - find the area between the graph of function and x-axis over the given ...
- Calculus - These are the two problems from my homework I don't get.. can you ...
- Functions, graphs - f(x)=(x+1)/(1+x^2) a) explain why the graph lies above the ...
- calculas - Use left and right endpoints and the given number of rectangles to ...
- Calculus - Use the Midpoint Rule with n = 4 to approximate the area of the ...
- Math: Calc 2 - Find the volume of the solid obtained by rotating the region ...
- integration - Find the area of the region under the graph of the function f on ...
- Calculus - Use the limit process to find the area of the region between the ...
- More Calc - Find the area between each curve and the x-axis for the given ...

More Related Questions