Answer:
Area covered by the fences will be 16.1 unit²
Step-by-step explanation:
Let the first parabola is represented by the function f(x) = 6x²
and second parabola by g(x) = x² + 9
point of intersection of the graphs will be determined when f(x) = g(x)
6x² = x² + 9
5x² = 9
x² = 1.8
x = ± 1.34
Now we will find the area between these curves drawn on the graph.
Area = [tex]\int_{-1.34}^{1.34}[f(x)-g(x)]dx=\int_{-1.34}^{1.34}[6x^{2}-(x^{2}+9)]dx[/tex]
= [tex]\int_{-1.34}^{1.34}(5x^{2}-9)dx[/tex]
= [tex][\frac{5}{3}x^{3}-9x]_{-1.34}^{1.34}[/tex]
= [tex][\frac{5}{3}(-1.34)^{3}-9(-1.34)-\frac{5}{3}(1.34)^{3}+9(1.34)][/tex]
= [tex][-4.01+12.06-4.01+12.06][/tex]
= 16.1 unit²
