8 trapezoids --> delta x = 1/8
x ______ y * f
0.0 1 * 1/2 ->.5
1/8 1.000976
1/4 1.00778
3/8 1.02603
1/2 1.06066
5/8 1.11541
3/4 1.19242
7/8 1.29225
8/8 1.41421*1/2 --> 0.707106
add them and multiply by 1/8
8.902633/8 =1.113
now do for rel
int (1+x^3)^.5 dx
= 1.11145
No, I used Wolfram, what a mess
see
http://www.wolframalpha.com/input/?i=integrate+%281%2Bx^3%29^.5+dx++from+x%3D0+to+1
error = 1.113 -1.111 = .002
or about 0.2 percent
Find the error resulting from approximation by Trapezoidal Rule:
integral (from 0 to 1) sqrt(1+ x^3) dx
.... compute the results for n=8
3 answers
Get it ?
Oh by the way, here is the recipe for the indefinite integral . put in
(1+x^3)^.5 dx
http://www.wolframalpha.com/input/?i=int+x^5+dx&lk=3
(1+x^3)^.5 dx
http://www.wolframalpha.com/input/?i=int+x^5+dx&lk=3
1 answer