- #1

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I kown top - bottom and right - left. but in here i am not sure what to do and what the boundaries are. can some one show me the work how to do this problem??? i am kinda confuse how to do this kind of problem with 3 curves. THANK YOU!!!

- Thread starter xstetsonx
- Start date

- #1

- 78

- 0

I kown top - bottom and right - left. but in here i am not sure what to do and what the boundaries are. can some one show me the work how to do this problem??? i am kinda confuse how to do this kind of problem with 3 curves. THANK YOU!!!

- #2

- 270

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So we need to solve 3 systems of equations. Once you have done that you can divide the region in to a true triangle and a curved slice. Find the areas of each separately.

- #3

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sorry still don't know what to do. my book doesn't have any examples like this question

- #4

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First find the points where the graph intersects to form the triangle by solving these three systems of equations:

System 1

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

[tex]y=3x[/tex]

A(x,y) =

System 2

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

[tex]y=9-x[/tex]

B(x,y) =

System 3

[tex]y=9-x[/tex]

[tex]y=3x[/tex]

C(x,y) =

Now you can break it in to two differences of integrals.

One from A to B and another from B to C.

- #5

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so when u say break it into 2 parts you mean (∫1.5958 on top, 1.4142 bottom (9-x)-(3x) dx)???? am i heading to the right direction??? if i am i don't know how to get the other part

- #6

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[tex]\int_{x_1}^{x_2}(x^3-3x) -\int_{x_1}^{x_2}3x[/tex]

Where x1 and x2 are the x values from the points A and B. then add that to the 2nd integral:

[tex]\int_{x_2}^{x_3}(9-x) -\int_{x_2}^{x_3}3x[/tex]

Where x2 and x3 are the x values from the points B and C.

Don't just take my word for it! Make certian you understand *why* --think about the region each integral represents, shade in the graph if needed.

The values you found look reasonable, but it looks like you used a graphing calculator? If I were teaching this course I'd want an exact value in radicals. Just check that your prof. is OK with aprox. values.

- #7

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- #8

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- #9

- 78

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oops wait a minute why do i get a negative value when i do ∫ x^3-3x? and the bonds are 1.5958 and 1.4142 right? shoulden't they all be positive?

nvm my mistake

nvm my mistake

Last edited:

- #10

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They should all be positive.

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