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-x^ -3x, - 8<xs 3 Find the total area of the region between the x-axis and the graph of y The total area of the region between the x-axis and the graph of y - x -3x, -8sxs3 is (Type an integer or a simplified fraction.)
Expert Answer
Given:
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у3-х* - 3х..(), -8<x<3
Calculation:
![The formula to find the area of the region between a curve f(x)and the x-axis on an interval
[a,b]is,
Here, f(x)x2 -3x, a -8 andb
3](https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/9da065e7-7c6d-4686-ba39-eef6f8e5dbcb/b52a1b8a-e6ab-4974-8a25-b33164755a02/lx9lk3jo.png)
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The formula to find the area of the region between a curve f(x)and the x-axis on an interval [a,b]is, Here, f(x)x2 -3x, a -8 andb 3
![To find the boundary points, we have to put y 0 in equation (1), we get
-x2 -3x 0
x23x 0
x(r+3) 0
-3
x 0 and x-
So the boundary points are [-8,-3], [-3,0] and [0,3]](https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/9da065e7-7c6d-4686-ba39-eef6f8e5dbcb/b52a1b8a-e6ab-4974-8a25-b33164755a02/usbiak.png)
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To find the boundary points, we have to put y 0 in equation (1), we get -x2 -3x 0 x23x 0 x(r+3) 0 -3 x 0 and x- So the boundary points are [-8,-3], [-3,0] and [0,3]
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