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d92292 Group Title

find the area enclosed between the curve y=x^3 and the line y=x

  • one year ago
  • one year ago

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  1. Algebraic! Group Title
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    did you sketch the region?

    • one year ago
  2. d92292 Group Title
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    im not sure on how to

    • one year ago
  3. Algebraic! Group Title
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    you're not sure how to sketch x^3 ?

    • one year ago
  4. d92292 Group Title
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    no i mean i sketched it, i dont know what to do after

    • one year ago
  5. Algebraic! Group Title
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    say, for example, you're asking about the area enclosed for positive values of x..: |dw:1355190249043:dw|

    • one year ago
  6. Algebraic! Group Title
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    you can see that it's the area under the line x (from 0 to 1) minus the area under x^3 (from 0 to 1)

    • one year ago
  7. Algebraic! Group Title
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    aka:\[\int\limits_{0}^{1} x-x ^{3} dx\]

    • one year ago
  8. Algebraic! Group Title
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    can you evaluate that integral?

    • one year ago
  9. d92292 Group Title
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    and then how do we find the anti derivitve of that hat

    • one year ago
  10. Algebraic! Group Title
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    the usual way:\[\int\limits_{ }^{ } x^n dx = \frac{ x^{n+1} }{ n+1 }\]

    • one year ago
  11. Algebraic! Group Title
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    so for \[\int\limits_{ }^{} x^1 dx\] \[\int\limits_{ }^{} x^1 dx = \frac{ x^{1+1} }{ 1+1}\]

    • one year ago
  12. Algebraic! Group Title
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    try it for x^3...

    • one year ago
  13. d92292 Group Title
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    x^4/4

    • one year ago
  14. Algebraic! Group Title
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    yes

    • one year ago
  15. Algebraic! Group Title
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    so \[\frac{ x^2 }{ 2 } -\frac{ x^4 }{4 } \]

    • one year ago
  16. Algebraic! Group Title
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    ok?

    • one year ago
  17. d92292 Group Title
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    and whats next?

    • one year ago
  18. Algebraic! Group Title
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    plug in the limts

    • one year ago
  19. Algebraic! Group Title
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    for the region on the interval x =0...+inf ( 1/2 -1/4 ) - (0/2 -0/4)

    • one year ago
  20. d92292 Group Title
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    kk

    • one year ago
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