Question

solve using the trapezoidal rule:

Answer 1

\[\int\limits_{0}^{1}\sqrt{1-x ^{2}}\]

by dividing into 5 parts

Answer 2

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

Answer 3

i know its a pretty easy question but my attempts don't match the answers at the back.

this is what i did:
\[\int\limits_{0}^{1}\sqrt{1-x ^{2}}\approx \int\limits_{0}^{1/5}\sqrt{1-x ^{2}}+ \int\limits_{1/5}^{2/5}\sqrt{1-x ^{2}}+ \int\limits_{2/5}^{3/5}\sqrt{1-x ^{2}}+ \int\limits_{3/5}^{4/5}\sqrt{1-x ^{2}}+ \int\limits_{4/5}^{1}\sqrt{1-x ^{2}}\]

Answer 4

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

Answer 5

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

Answer 6

oh ok
http://en.wikipedia.org/wiki/Trapezoidal_rule

= (1)(1/2) = 1/2

Answer 7

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

Answer 8

hi can u help me after her

Answer 9

yeh, simple

Answer 10

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

Answer 11

general trapezodial rule

Answer 12

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

Answer 13

i used that

Answer 14

by dividing into 5 intervals as it asks

Answer 15

now, diving into 5 sections means using 6 function values

Answer 16

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

Answer 17

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

Answer 18

ok lol

Answer 19

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