Thread: Area problem by using the Trigonometric Substitution

Let R be the smaller of the two regions enclosed by the elipse 169x^2 +100y^2=16900 and the line x= 5 squar root of (2).

Find the area of the region R.


thanks!~

Originally Posted by shannon1111

Let R be the smaller of the two regions enclosed by the elipse 169x^2 +100y^2=16900 and the line x= 5 squar root of (2).

Find the area of the region R.


thanks!~

The ellipse is centered at the origin, stretched in the y-direction, and intersects with the vertical line at:




Solving for x from the ellipse's upper half, in terms of y




The equation above represents the curve to the right. The curve to the left is simply:


Setup the integral now as
INTEGRAL (X_right - X_left) dy where y ranges from 0 to

After you find the integral remember to multiply it by two to account for the other half of the area below the horizontal axis.

I hope this helps.