2. Determine the area of the ellipse x²/4 + y²/9 =1 using method of integration.

To determine the area of the ellipse \( \frac{x^2}{4} + \frac{y^2}{9} = 1 \) using integration, we follow these steps:

1. **Rewrite the equation of the ellipse in a standard form:**

   The given equation is
   \[
   \frac{x^2}{4} + \frac{y^2}{9} = 1
   \]
   which is the equation of an ellipse in standard form \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \), where \( a^2 = 4 \) and \( b^2 = 9 \). Therefore, \( a = 2 \) and \( b = 3 \).

2. **Set up the formula for the area of the ellipse:**

   The area of an ellipse can be calculated using double integration:
   \[
   A = \int \int_{\text{Ellipse}} dA
   \]
   In Cartesian coordinates, \( dA = dx \, dy \).

   To simplify the computation

Determine the area of the ellipse x²/4 + y²/9 =1 using the method of integration.

Learn how to calculate the area of the ellipse x²/4 + y²/9 = 1 using integration. This problem involves calculus concepts, including double integration and geometric formulas for ellipses. Suitable for students in Grades 11-12 and college-level calculus courses.

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