Area under a curve

Feb 2010
155
3
United States
Find the area under the graph to the x axis from -2 to 2 for

f(x) = (4 - x^2)^(1/2)


Okay, so I understand how to do the problem overall but I don't know how to take the antiderivative of that particular function. Is there an easy way to do the chain rule in reverse or what...
 
Last edited:

Ackbeet

MHF Hall of Honor
Jun 2010
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Is that \(\displaystyle f(x)=\sqrt{4-x^{2}}\)? If so, I wouldn't integrate. You can solve the problem without integrating. Think about what the shape of that curve is.
 
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Feb 2010
155
3
United States
Yeah, that's the function. It's a semicircle?
 

Ackbeet

MHF Hall of Honor
Jun 2010
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I asked my question because you seemed unsure of whether it's a semicircle or not. If you are sure, then what do you get for the area under it?
 
Feb 2010
155
3
United States
Oh, sorry. I had the question mark there because I didn't know where you were going with it, not whether or not it's a semicircle. Um...I don't really know. It's doesn't quite touch the x-axis according to my graphing calculator, and as a result it is sort of messing with all of the estimations I've attempted, and I don't know how to integrate a function like that.
 

Ackbeet

MHF Hall of Honor
Jun 2010
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Are you required to solve this problem using integration? Because I find that simply writing the answer down is a lot easier. What's the radius of this semicircle? And what's the area of a semicircle in general?
 
Jul 2007
894
298
New Orleans
Follow Ackbeet's advice. Integration is just the area under the curve so...
 
Feb 2010
155
3
United States
I think integration is preferred, but this method should suffice.