# Thread: definite integral

1. ## definite integral

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

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

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

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

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

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

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

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

and so on and so forth

3. im not getting 71/6; im getting 94/9 can you see what im doing wrong

4. Originally Posted by vinson24
im not getting 71/6; im getting 46/9 can you see what im doing wrong
$x_1^* = \frac 43,~x_2^* = \frac 83,~\text{and }x_3^* = 4$

do you see why?

do you get the answer now? what are you using for f(x)? the function you have at the end?

5. 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

6. 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.

7. its the right section and thats the whole problem this problem is in the section of definite integrals