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anonymous

  • 5 years ago

solve using the trapezoidal rule:

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  1. anonymous
    • 5 years ago
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    \[\int\limits_{0}^{1}\sqrt{1-x ^{2}}\] by dividing into 5 parts

  2. dumbcow
    • 5 years ago
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    couldn't you use trig substitution = sin^-1 (x) +C

  3. anonymous
    • 5 years ago
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    i know its a pretty easy question but my attempts don't match the answers at the back. this is what i did: \[\int\limits_{0}^{1}\sqrt{1-x ^{2}}\approx \int\limits_{0}^{1/5}\sqrt{1-x ^{2}}+ \int\limits_{1/5}^{2/5}\sqrt{1-x ^{2}}+ \int\limits_{2/5}^{3/5}\sqrt{1-x ^{2}}+ \int\limits_{3/5}^{4/5}\sqrt{1-x ^{2}}+ \int\limits_{4/5}^{1}\sqrt{1-x ^{2}}\]

  4. anonymous
    • 5 years ago
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    but i have to use the trapezoidal rule as i will be assessed on it lol

  5. anonymous
    • 5 years ago
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    then following from above : \[\approx1/10(1+\sqrt{24}/5)+1/10(\sqrt{24}/5+\sqrt{21}/5)+1/10(\sqrt{21}/5+4/5)+1/10(4/5+3/5)+1/10(3/5+0)\]

  6. dumbcow
    • 5 years ago
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    oh ok http://en.wikipedia.org/wiki/Trapezoidal_rule = (1)(1/2) = 1/2

  7. anonymous
    • 5 years ago
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    i actually understand the rule but i cant see where ive gone wrong in my working after attempting numerous times

  8. toxicsugar22
    • 5 years ago
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    hi can u help me after her

  9. anonymous
    • 5 years ago
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    yeh, simple

  10. anonymous
    • 5 years ago
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    \[A= \frac{h}{2} ( f(x0) + 2 [ f(x1) + f(x2) + .....+ f(x(n-1)] + f(xn) ) \]

  11. anonymous
    • 5 years ago
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    general trapezodial rule

  12. anonymous
    • 5 years ago
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    which is the same as \[\int\limits_{a}^{b}f(x)\approx b-a/2(f(a)+f(b))\]

  13. anonymous
    • 5 years ago
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    i used that

  14. anonymous
    • 5 years ago
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    by dividing into 5 intervals as it asks

  15. anonymous
    • 5 years ago
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    now, diving into 5 sections means using 6 function values

  16. anonymous
    • 5 years ago
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    i used from 0, 1/5, 2/5, 3/5, 4/5, 1

  17. anonymous
    • 5 years ago
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    god this is slow, im going to post the answer as a question

  18. anonymous
    • 5 years ago
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    ok lol

  19. anonymous
    • 5 years ago
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    if it makes a difference this is the exact wording of the question use the trapezoidal rule with five function values to estimate \[\int\limits_{0}^{1}\sqrt{1-x ^{2}}\] to four decimal places

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