Find the areas of the regions whose boundaries are given

  • Thread starter duki
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  • #1
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I have three questions:

Homework Statement



Find the areas of the regions whose boundaries are given.

Homework Equations



[tex]y=x^3-3[/tex]
[tex]y=1[/tex]

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



[tex]y^2=x[/tex]
[tex]x+y=2[/tex]

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



[tex]y=x^3-2x^2-3x[/tex]
[tex]y=0[/tex]

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! :)
 

Answers and Replies

  • #2
Dick
Science Advisor
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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.
 
  • #3
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many apologies... it should have been x^2-3
 
  • #4
HallsofIvy
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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 [itex]\int [1- (x^2-3)]dx= \int (4- x^2)dx[/itex]. That, integrated between -2 and 2, is positive.
 
  • #5
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And for the last problem, you would have two different enclosed areas. One would be between -1 and 0 and the other between 0 and 3.
This means you would have to set up 2 different equations and find the sum of the areas.
HINT: The equations are very similiar just siwtched in order.
 

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