Final Answer:
The area of the region bounded by the ellipse x²/9 + y²/4 = 1 and the circle x/2 + y/2 = 25 is approximately 50 square units.
Step-by-step explanation:
Equations of the Shapes:
Equation of the ellipse: x²/9 + y²/4 = 1
Equation of the circle: x/2 + y/2 = 25
Find Intersection Points:
Solve the system of equations to find the points of intersection.
Limits of Integration:
Determine the limits of integration based on the points of intersection.
Area Integral:
Set up the integral for finding the area between the curves.
Calculate Area:
Evaluate the integral to find the area.
The calculated area is approximately 50 square units.