Homework Help

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

user profile pic

carolinesmiths | Student, Kindergarten | Salutatorian

Posted August 31, 2012 at 5:43 AM via web

dislike 1 like

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

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 31, 2012 at 5:54 AM (Answer #1)

dislike 1 like

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

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes