# Find the areas of the regions whose boundaries are given

I have three questions:

## Homework Statement

Find the areas of the regions whose boundaries are given.

## Homework Equations

$$y=x^3-3$$
$$y=1$$

## The Attempt at a Solution

x=-2, x=2
I got -10.67 but I know this can't be true because you can't have a negative area.

## Homework Statement

Find the areas of the regions whose boundaries are given.

## Homework Equations

$$y^2=x$$
$$x+y=2$$

## The Attempt at a Solution

y=1, y=-2
I got -4.5, but again that can't be right because it's negative :(

## Homework Statement

Find the areas of the regions whose boundaries are given.

## Homework Equations

$$y=x^3-2x^2-3x$$
$$y=0$$

## The Attempt at a Solution

I got to x=0, x=-1, and x=3 but I don't know where to go from here.

Thanks for any help! :)

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Dick
Homework Helper
Let's just start with the first one. How did you get x=-2, x=2 or was that given? The curves y=x^3-3 and y=1 don't enclose any bounded region.

many apologies... it should have been x^2-3

HallsofIvy
If you get a negative area then you have the two functions in the wrong order. For x between -2 and 2, the graph of x2- 3 is below the graph of y= 1. You should be integrating $\int [1- (x^2-3)]dx= \int (4- x^2)dx$. That, integrated between -2 and 2, is positive.