Area under a curve

bobsanchez

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...

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Ackbeet

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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.

mr fantastic

bobsanchez

Yeah, that's the function. It's a semicircle?

Ackbeet

MHF Hall of Honor

bobsanchez

It just is. What do you mean?

Ackbeet

MHF Hall of Honor
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?

bobsanchez

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
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?

11rdc11

Follow Ackbeet's advice. Integration is just the area under the curve so...

bobsanchez

I think integration is preferred, but this method should suffice.