# How do we find the area inside the cardioid #f(theta)=a(1+costheta)#?

Area of the region inside cardioid is

Area inside the cardioid or any other bound curve is found using integral

Hence, substituting (B) in (A)

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To find the area inside the cardioid defined by the polar equation ( f(\theta) = a(1 + \cos \theta) ), you integrate the function ( \frac{1}{2} f(\theta)^2 ) with respect to ( \theta ) over the appropriate interval. This integral gives the area within one loop of the cardioid. The bounds of integration depend on the number of loops you want to find the area for. For one loop, typically you integrate from ( 0 ) to ( 2\pi ).

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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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