Question

How do I find the exact value of this question? Find the area between y= x sqrt(1-x^2) and the x-axis.

Answer 1

@zepdrix

Answer 2

=0

Answer 3

It is an odd function, hence integral on the whole domain =0

Answer 4

Algebraic way: the function defined on [-1,1], hence the integral is
\[\int_{-1}^1 x\sqrt{(1-x^2)}dx =0\]

Answer 5

:)

Answer 6

`Find the area between y= x sqrt(1-x^2) and the x-axis.`
I didn't read correctly (LaTeX markup would help). \(y = x\sqrt{1-x^2}\).

Answer 7

Maybe I phrased the question wrong. o_O Lemme post it.

Answer 8

https://snag.gy/pMqjnf.jpg

Answer 9

@reemii I failed!!

Answer 10

https://snag.gy/O8kG1I.jpg

Answer 11

There's the answer, but I need it explained...o_o

Answer 12

Then -and that's always an assumption that isn't written- are we considering negative areas or not.
It's different from your previous qestion, in which there were negative areas.

Now, all areas are positive. The only clue to understanding the question correctly would be `total area` . "TOTAL" -> only positive?

Answer 13

Usually:
But in a "total area" problem:

.. seems like it. Since the shape of the curve is the same on both sides of 0, the total area is twice the area of the right side.