Question

trapezoidal rule of

integral from 0 to 1 of e^(-6x^2)dx n=4

I got 2.016753867... and it says it's wrong.

I split it up as..
delta x/2=1/8
x_0=0
x_1=0.25
x_2=0.50
x_3=0.75
x_4=1

help?

Answer 1

nevermind :) got it!

Answer 2

I inputted the function wrong..

Answer 3

so if you draw it

I've calcuated the function values and they are on top of the offset.



and from here you can just apply the formula for area of each trapeziod then sum the areas...

I've always hated the formula.

Answer 4

but if you want to use the formula you would have

\[\int\limits_{0}^{1}e^{-6x^2} dx \approx \frac{0.5}{2}[1 + 2 \times 0.687289 + 2 \times 0.22313+ 2 \times 0.034218 + 0.002479]\]

and its just a case of evaluating.

Answer 5

oops should be

\[\frac{0.25}{2}\]

at the start

Answer 6

i got 0.361469

Answer 7

yeah I figured it out. Thanks.