Question

using left hand endpoints with 2 subintervals, approximate integral [0,1] (1/1+x^2)dx

Answer 1

\[\int\limits_{0}^{1} 1\div \left( 1+x^{2} \right) dx\]

Answer 2

oh man i really don't feel like doin any math right now.. but seems like u need help and nobody's helpin.. i guess ill try this..

Answer 3

do you have the selection answers?

Answer 4

Okay so first of all it says two sub intervals right ..and your integral is from 0 to 1, or the length is 1. So each of the steps will be:
1 / 2 = 0.5

Answer 5

\[x _{0}=0\] since we are starting from 0
so:
\[x _{0}=0\]
\[x _{1}=0.5\]
\[x _{2}=1\]

Answer 6

As you can see, each step is the previous one plus 0.5

Answer 7

1) \[f(x _{0}) = 1/(1+0^2) = 1\]

Answer 8

2) \[f(x _{1}) = 1/(1+0.5^2)\]

Answer 9

=0.8

Answer 10

3) \[f(x_2)=1/(1+1^2) = 1/2\]

Answer 11

Now to approximate the integral: use:
\[h*(f(x_0)+f(x_1)+f(x_2))\]

Answer 12

where h is the step size or 0.5

Answer 13

So you end up with:
0.5 ( 1 + 0.8 + 0.5 ) = 0.5 * 2.3 = 1.15

Answer 14

The actual answer is 0.785 or pi/4, but we are so off because we only have 2 steps.. the more steps you have or the less the step size, the better is ur answer.

Answer 15

ah we are looking for the LH... n=2, deltax=(1-0)/2=1/2=.5
LH=(1/2)(1+.8)=.9 answer and for the
RH=(1/2)(.8+.5)=13/20=.65

Answer 16

mark you are wrong.. you didn't add the last step.. you did from 0 to 1/2

Answer 17

then he needs 1/2 to 1.. which will be:
(1/2) ( 1 + .8 + .5) = 1.15

Answer 18

nope,, the LH rule is up to .5only, and for the RH rule is up to 1

Answer 19

n= 0 ,5 1
f(x)= 1 .8 .5

Answer 20

http://www.mathsnetalevel.com/question.php?ref=3805

Answer 21

follow the steps and see how it goes..

Answer 22

i think i got it from here just needed a refresher. thanks guys!

Answer 23

LH=(delta x)(f(0)+f(.5))=.5(1+.8)= .9 and for the RH
RH=(deltax)(f(.5)+f(1))=.5(.8+.5)=.65

Answer 24

ok have fun guys......thnx