# How do you determine the area enclosed by an ellipse #x^2/5 + y^2/ 3# using the trapezoidal rule?

Assuming that the ellipse is

The upper half of the ellipse is described by the function

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To determine the area enclosed by the ellipse ( \frac{x^2}{5} + \frac{y^2}{3} = 1 ) using the trapezoidal rule, we first need to approximate the curve by dividing it into small segments and approximating each segment as a trapezoid.

- Divide the ellipse into ( n ) equal segments along the x-axis.
- Calculate the corresponding y-values for each segment using the equation of the ellipse: ( y = \sqrt{3(1 - \frac{x^2}{5})} ).
- Approximate each segment as a trapezoid by connecting consecutive points with straight lines.
- Calculate the area of each trapezoid using the formula for the area of a trapezoid: ( A = \frac{1}{2}(b_1 + b_2)h ), where ( b_1 ) and ( b_2 ) are the lengths of the parallel sides and ( h ) is the height (the width of each segment along the x-axis).
- Sum up the areas of all trapezoids to obtain an approximation of the total area enclosed by the ellipse.

The more segments you use (i.e., the larger the value of ( n )), the more accurate your approximation will be.

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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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