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mathstina

  • 2 years ago

Evaluate the integral ∬sin(x^2+y^2 )dA where R is the region that lies above the x-axis within the circle x^2 +y^2 =16 by changing into polar coordinates.

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  1. mathstina
    • 2 years ago
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    as for radius is from -4 to 4. for angle is from 0 to 180 ?

  2. experimentX
    • 2 years ago
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    yep!!

  3. mathstina
    • 2 years ago
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    differentiate by r dr dθ ?

  4. experimentX
    • 2 years ago
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    use radiant (0 to pi)!! and dA = r dr d(theta)

  5. mathstina
    • 2 years ago
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    ok. let me work out....

  6. experimentX
    • 2 years ago
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    \[ \int_0^4 \int_0^\pi \sin ( r^2 \cos^2 \theta + r^2 \sin^2 \theta) \; r \; dr\; d\theta \]

  7. mathstina
    • 2 years ago
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    could u pls explain to me why e radius is from 0 to 4 nt -4 to 4? and hw to get e function?

  8. mathstina
    • 2 years ago
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    ok i understood. hw abt e integration part?

  9. experimentX
    • 2 years ago
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    \[ \int_0^4 \int_0^\pi \sin ( r^2) \; r \; d\theta\; dr\ \\ \int_0^4 \sin ( r^2) \; r \; \left [ \theta \right ]_0^\pi dr\\ \] just use subs r^2 = u

  10. mathstina
    • 2 years ago
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    ok...thanks. let me work out

  11. mathstina
    • 2 years ago
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    is the ans \[- \pi \cos8

  12. mathstina
    • 2 years ago
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    \[-\pi \cos 8\]

  13. mathstina
    • 2 years ago
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    am i right??

  14. experimentX
    • 2 years ago
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    http://www.wolframalpha.com/input/?i=Integrate[Integrate[Sin[r^2]r%2C+{theta%2C+0%2C+pi}]%2C+{r%2C0%2C+4}] check it out again

  15. experimentX
    • 2 years ago
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    Integrate[Integrate[Sin[r^2]r, {theta, 0, pi}], {r,0, 4}]

  16. mathstina
    • 2 years ago
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    hw?

  17. mathstina
    • 2 years ago
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    i need guidance pls...

  18. experimentX
    • 2 years ago
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    |dw:1353425265831:dw|

  19. experimentX
    • 2 years ago
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    do your integration and arrive at \[ \pi [ \cos 0 - \cos 16] \over 2\\ = {\pi(1 - \cos 16) \over 2 }\]just use half angle formula

  20. mathstina
    • 2 years ago
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    do i need to use mehod by substitution for r^2

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