## anonymous 5 years ago solve using the trapezoidal rule:

1. anonymous

$\int\limits_{0}^{1}\sqrt{1-x ^{2}}$ by dividing into 5 parts

2. anonymous

couldn't you use trig substitution = sin^-1 (x) +C

3. anonymous

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

4. anonymous

but i have to use the trapezoidal rule as i will be assessed on it lol

5. anonymous

then following from above : $\approx1/10(1+\sqrt{24}/5)+1/10(\sqrt{24}/5+\sqrt{21}/5)+1/10(\sqrt{21}/5+4/5)+1/10(4/5+3/5)+1/10(3/5+0)$

6. anonymous

oh ok http://en.wikipedia.org/wiki/Trapezoidal_rule = (1)(1/2) = 1/2

7. anonymous

i actually understand the rule but i cant see where ive gone wrong in my working after attempting numerous times

8. toxicsugar22

hi can u help me after her

9. anonymous

yeh, simple

10. anonymous

$A= \frac{h}{2} ( f(x0) + 2 [ f(x1) + f(x2) + .....+ f(x(n-1)] + f(xn) )$

11. anonymous

general trapezodial rule

12. anonymous

which is the same as $\int\limits_{a}^{b}f(x)\approx b-a/2(f(a)+f(b))$

13. anonymous

i used that

14. anonymous

by dividing into 5 intervals as it asks

15. anonymous

now, diving into 5 sections means using 6 function values

16. anonymous

i used from 0, 1/5, 2/5, 3/5, 4/5, 1

17. anonymous

god this is slow, im going to post the answer as a question

18. anonymous

ok lol

19. 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