This is a challenging question.
Please help me think about it.
Consider the two regions bounded by the circle x^2 +y^2 = 8 and the parabola y^2 = 2*x.
Find their areas.
attached question.

Question

anonymous · Answer

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anonymous · Answer

So, find the areas of each induvidually correct?

anonymous · Answer

we need to find where these two function cross

anonymous · Answer

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anonymous · Answer

A unclear question. two parts of bounded areas I guess. another symmetry

anonymous · Answer

Yea, this has symmetry. We'll just find the area in quadrant 1 then double it

anonymous · Answer

To find our limits of integration we set the two equations equal to one another. They will cross at those x values

anonymous · Answer

I agree. the intersection is x = 2

anonymous · Answer

$$y=\sqrt{8-x^2} and y=\sqrt{2x}$$
so,
$$\sqrt{8-x ^{2}}=\sqrt{2x}$$

anonymous · Answer

oh you got it already

anonymous · Answer

Now due to the nature of integration, it will be easier to integrate the parabaloid function with respect to x

anonymous · Answer

Is the attached the correct approach?

anonymous · Answer

No, you will only have a single integration to do. Just integrate the parabaloid function

anonymous · Answer

with those limits. 0...2

anonymous · Answer

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