# How do you find the area of the region bounded by the polar curves #r=sqrt(3)cos(theta)# and #r=sin(theta)# ?

The area of the enclosed region is

It looks like this:

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To find the area of the region bounded by the polar curves ( r = \sqrt{3}\cos(\theta) ) and ( r = \sin(\theta) ), you need to compute the definite integral of the difference between the outer curve ( r = \sin(\theta) ) and the inner curve ( r = \sqrt{3}\cos(\theta) ) over the interval where they intersect. This intersection occurs when ( \sqrt{3}\cos(\theta) = \sin(\theta) ). Solve this equation to find the bounds of integration. Then integrate the difference of the outer curve squared minus the inner curve squared over this interval with respect to ( \theta ). This will give you the area of the region.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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