area of ellipse- calculus

find the area of the ellipse (x+2y)2 + (3x+4y)2 =1

to find the area of the ellipse is to find the area of the under the curve.  this means that you need to find the definite integral of the function y with respect to x.
 
 
first, find the x-intercepts of this equation.  the x-intercepts will serve as your bounds. 
 
then, you will solve for y explicitly from the equation of the ellipse.
 
lastly, you will take the integral of y with respect to x.  you will evaluate the definite integral using the bounds.  the negative x-intercept will be your lower bound.  the positive x-intercept will be your upper bound.
 
 
as a last step, multiply the result of the definite integral by 2.
 
 
got it!