Question

Calculate an approximate value of the area of the place inside the curve. (So if you sketch it up (by using WolframAlpha or something else) then you will see that what is sought after is the calculated value of the area that is inside the curve

1 = (40+43)x^2y^2 + y^4 + (1+1)x^4

Answer 1

Clearly the curve is symmetric about both x and y, hence its curve will be symmetric in alll 4 quadrants. Notice the x and yintercepts by putting y = 0, x = 0 respectively

With these limits, we have a fairly good idea that curve will be bounded inside these bounds. The exact curve can be traced below using Desmos

Now let us express y in terms of x, the function that needs to be integrated

We can integrate this function (with positivr sign) from x = 0 to x = 2^(-0.25) ≈ 0.840896415, the x-intercept, and make that 4 times to get the required area. Obviously we need to invoke Wolfram Apfa to help us here