What is the area bound by y = x^2 - 4 and the x-axis.

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Math

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The area bound by the curve y = x^2 - 4 and the x-axis has to be determined. First determine the point of intersection of the two, this requires solving x^2 - 4 = 0

=> x^2 = 4

=> x = 2 and x = -2

The area to be determined is the integral `int_(-2)^2 (x^2 -4) dx`

=> `x^3/3- 4x |_(-2)^(2)`

=> `8/3 - 8 + 8/3 - 8`

As the area cannot be negative take the absolute value of -32/3 which is 32/3.

The area enclosed by y = x^2 - 4 and the x-axis is 32/3

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