anonymous
  • anonymous
solve using the trapezoidal rule:
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
\[\int\limits_{0}^{1}\sqrt{1-x ^{2}}\] by dividing into 5 parts
dumbcow
  • dumbcow
couldn't you use trig substitution = sin^-1 (x) +C
anonymous
  • anonymous
i know its a pretty easy question but my attempts don't match the answers at the back. this is what i did: \[\int\limits_{0}^{1}\sqrt{1-x ^{2}}\approx \int\limits_{0}^{1/5}\sqrt{1-x ^{2}}+ \int\limits_{1/5}^{2/5}\sqrt{1-x ^{2}}+ \int\limits_{2/5}^{3/5}\sqrt{1-x ^{2}}+ \int\limits_{3/5}^{4/5}\sqrt{1-x ^{2}}+ \int\limits_{4/5}^{1}\sqrt{1-x ^{2}}\]

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anonymous
  • anonymous
but i have to use the trapezoidal rule as i will be assessed on it lol
anonymous
  • anonymous
then following from above : \[\approx1/10(1+\sqrt{24}/5)+1/10(\sqrt{24}/5+\sqrt{21}/5)+1/10(\sqrt{21}/5+4/5)+1/10(4/5+3/5)+1/10(3/5+0)\]
dumbcow
  • dumbcow
oh ok http://en.wikipedia.org/wiki/Trapezoidal_rule = (1)(1/2) = 1/2
anonymous
  • anonymous
i actually understand the rule but i cant see where ive gone wrong in my working after attempting numerous times
toxicsugar22
  • toxicsugar22
hi can u help me after her
anonymous
  • anonymous
yeh, simple
anonymous
  • anonymous
\[A= \frac{h}{2} ( f(x0) + 2 [ f(x1) + f(x2) + .....+ f(x(n-1)] + f(xn) ) \]
anonymous
  • anonymous
general trapezodial rule
anonymous
  • anonymous
which is the same as \[\int\limits_{a}^{b}f(x)\approx b-a/2(f(a)+f(b))\]
anonymous
  • anonymous
i used that
anonymous
  • anonymous
by dividing into 5 intervals as it asks
anonymous
  • anonymous
now, diving into 5 sections means using 6 function values
anonymous
  • anonymous
i used from 0, 1/5, 2/5, 3/5, 4/5, 1
anonymous
  • anonymous
god this is slow, im going to post the answer as a question
anonymous
  • anonymous
ok lol
anonymous
  • anonymous
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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