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Svetllana [295]
3 years ago
10

More on Areas. Farmer Jones, and his wife, Dr. Jones, both mathematicians, decide to build a fence in their field to keep the sh

eep safe. Being mathematicians, they decide that the fences are to be in the shape of the parabolas y=6x2 and y=x2+9. What is the area of the enclosed region?
Mathematics
1 answer:
Olin [163]3 years ago
6 0

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 = \int_{-1.34}^{1.34}[f(x)-g(x)]dx=\int_{-1.34}^{1.34}[6x^{2}-(x^{2}+9)]dx

= \int_{-1.34}^{1.34}(5x^{2}-9)dx

= [\frac{5}{3}x^{3}-9x]_{-1.34}^{1.34}

= [\frac{5}{3}(-1.34)^{3}-9(-1.34)-\frac{5}{3}(1.34)^{3}+9(1.34)]

= [-4.01+12.06-4.01+12.06]

= 16.1 unit²

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