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I'm taking a probability class where multivariate calculus was not a prerequisite, but some of it is coming up, I get the concept of, say integrating over a region, but get lost in some of the mechanics

Here is the problem (I don't want a full solution):

A point is uniformly distributed within the disk of radius 1. That is its density is

[itex]

f(x,y) = C \hspace{1cm} 0 \leq x^2 + y^2 \leq 1

[/itex]

Find the probability that its distance from the origin is less than x, 0 \leq x \leq 1

I'm pretty sure I have to set up an integral that integrates over a disc of radius x to get the probability

Something like this

[itex]

\int_A \int_B C \, dx \, dy

[/itex]

But I don't know what the intervals A and B are supposed to be.

Can someone point me in the right direction? I get confused because my attempts end up with x being involved in the limit of integration, but x is the dummy variable, which doesn't seem right.

Here is the problem (I don't want a full solution):

A point is uniformly distributed within the disk of radius 1. That is its density is

[itex]

f(x,y) = C \hspace{1cm} 0 \leq x^2 + y^2 \leq 1

[/itex]

Find the probability that its distance from the origin is less than x, 0 \leq x \leq 1

I'm pretty sure I have to set up an integral that integrates over a disc of radius x to get the probability

Something like this

[itex]

\int_A \int_B C \, dx \, dy

[/itex]

But I don't know what the intervals A and B are supposed to be.

Can someone point me in the right direction? I get confused because my attempts end up with x being involved in the limit of integration, but x is the dummy variable, which doesn't seem right.

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