# definite integral

• Nov 16th 2008, 04:24 PM
vinson24
definite integral
find the value of
a)$\displaystyle A \approx \sum_{k = 1}^{n} f(x_{k}^*) \Delta x$

b)max
$\displaystyle \Delta{x_{k}}$

f(x)=x+1; a=0,b=4; n=3;
$\displaystyle Deltax_1=1,\ Deltax_2=1,\ Deltax_3=2\$
$\displaystyle {x_{1}^*}=1/3,\ {x_{2}^*}=3/2,\ {x_{3}^*}=3$

• Nov 16th 2008, 04:37 PM
Jhevon
Quote:

Originally Posted by vinson24
find the value of
a)$\displaystyle A \approx \sum_{k = 1}^{n} f(x_{k}^*) \Delta x$

b)max
$\displaystyle \Delta{x_{k}}$

f(x)=x+1; a=0,b=4; n=3;
$\displaystyle Deltax_1=1,\ Deltax_2=1,\ Deltax_3=2\$
$\displaystyle {x_{1}^*}=1/3,\ {x_{2}^*}=3/2,\ {x_{3}^*}=3$

as written, these are not questions to be answered by definite integrals, as these are not Riemann sums.

here you have n = 3, so you just want

$\displaystyle A \approx \sum_{n = 1}^3 f(x_k^*) \Delta x = \Delta x \sum_{n = 1}^3 f(x_k^*) = \frac 43 [f(x_1^*) + f(x_2^*) + f(x_3^*)] = \cdots$

and so on and so forth
• Nov 16th 2008, 04:44 PM
vinson24
im not getting 71/6; im getting 94/9 can you see what im doing wrong
• Nov 16th 2008, 04:52 PM
Jhevon
Quote:

Originally Posted by vinson24
im not getting 71/6; im getting 46/9 can you see what im doing wrong

$\displaystyle x_1^* = \frac 43,~x_2^* = \frac 83,~\text{and }x_3^* = 4$

do you see why?

do you get the answer now? what are you using for f(x)? the function you have at the end?
• Nov 16th 2008, 04:55 PM
vinson24
i take each of those numbers and substitute them into x+1 and then take the sum of them and multiply the sum of those by 4/3 but i dont get the answer 71/6 also im getting 5/2 for x*2
• Nov 16th 2008, 05:31 PM
Jhevon
Quote:

Originally Posted by vinson24
i take each of those numbers and substitute them into x+1 and then take the sum of them and multiply the sum of those by 4/3 but i dont get the answer 71/6 also im getting 5/2 for x*2

x_1 starts at 4/3 and you add 4/3 to that to get x_2 and then 4/3 to that to get x_3

make sure you are looking in the right section for the answer. something seems amiss here.
• Nov 16th 2008, 05:39 PM
vinson24
its the right section and thats the whole problem this problem is in the section of definite integrals