Answer :
The area of the region in the first quadrant bounded on the left and right by the two given graphs is; A: 2.983
What is the area bounded by the graph?
We are given the equations;
x = y⁴ + y² ----(eq 1)
x = 5y ----(eq 2)
Now, let us put eq 1 into eq 2 to get;
y⁴ + y² = 5y
y⁴ + y² - 5y = 0
Using online roots of polynomial calculator, we have;
y = 0 and 1.516
Thus, the area of the region will be gotten by finding the integral between those two points;
[tex]\int\limits^0_\frac{1.516}{} {y^{4} + y^{2} - 5y} \, dy[/tex]
Integrating this, we have;
[tex]\left[\begin{array}{ccc}y^{4} +y^{2} - 5y\\\\\end{array}\right]^{0}_{1.516}[/tex]
Plugging in the relevant values and subtracting gives;
Area = 2.98276 ≈ 2.983
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