Question

Am I doing this right? (Trapezoidal Rule)

Answer 1

\[\int\limits_{0}^{2} x^2dx\]
\[\frac{ 2 }{ 2(4) } (2)(1+4)\]
\[\frac{ 1 }{ 2 } (5) \]
\[= 2.5\]

Answer 2

What is your "n" given value?

Answer 3

oh sorry
n=4

Answer 4

So your midpoints (∆x) are:

[0,0.5][0.5,1][1,1.5][1.5,2]

b/c your given bounds are from 0 to 2.

Answer 5

uhh, what midpoints?

Answer 6

Sorry, subintervals.

Answer 7

sorry, why would you need subintervals? cuz my textbook says nothing about that.

Answer 8

ohhhh i see

Answer 9

Then you just plug in those values into:

\[\int\limits_{a}^{b}f(x)dx \approx \frac{ ∆x }{ 2 }[f(x_0)+2f(x_1)+2f(x_2)+...=2f(x_{n-1})+f(x_n)]\]

Answer 10

yeah i understand what i did wrong now....

Answer 11

I hope this clears things up.

Answer 12

Note that all the function evaluations, with the exception of the first and last, are multiplied by 2. Just so you can remember.

Answer 13

i got the same answer when i divided it...

Answer 14

ok. Whatever works. Best of luck :)

Answer 15

oh just kidding my mistake..