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anonymous

  • 5 years ago

What is a strategy to evaluate INT(sqrt(a-x^2)dx) ?

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  1. anonymous
    • 5 years ago
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    put x= a sin(t)

  2. anonymous
    • 5 years ago
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    i'm the least experienced with trig substitution, can you show me the next step? my problem is that i keep ending up with two terms under the sqrt and they don't make another trig identity.

  3. anonymous
    • 5 years ago
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    x= a sin(t) dx/dt= a cost

  4. anonymous
    • 5 years ago
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    dx= a cost dt

  5. anonymous
    • 5 years ago
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    i imagine what i'm trying to get is a trig function squared under the square root so that they cancel, is there another way that would get rid of that square root?

  6. anonymous
    • 5 years ago
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    here is what u get

  7. anonymous
    • 5 years ago
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    hey in ur question is it a or a^2?

  8. anonymous
    • 5 years ago
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    a

  9. anonymous
    • 5 years ago
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    ok...do integration by parts..u know how to do that.......I've done it on paper ..it works

  10. anonymous
    • 5 years ago
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    so x=sin (t), and int by parts as well?

  11. anonymous
    • 5 years ago
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    no just integration by parts without any substitution

  12. anonymous
    • 5 years ago
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    so u=a-x^2 and dv=sqrt(u)du ?

  13. anonymous
    • 5 years ago
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    dont substitute, take the whole square root thing as first term and 1 as second term. okay?

  14. anonymous
    • 5 years ago
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    i don't get it, it just seems to prolong the problem. i still have two terms under the sqrt.

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