Question

Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral.

http://tinypic.com/r/2ldwvoi/8

Answer 1

?? i really dont know this sorry but good luck \(\large\cal\color{red}=\color{red})\)

Answer 2

Thanks @Muzzack . :)

Answer 3

my pleasure :)

Answer 4

http://www.mathwords.com/t/trapezoid_rule.htm

Answer 5

\[\large \int \limits_0^8 \sqrt[3]{x}~dx = \dfrac{\Delta x}{2}\left[f(1) + 2f(2) + \cdots + 2f(7) +f(8)\right]\]

Answer 6

\(\Delta x = \dfrac{b-a}{n} = \dfrac{8-0}{8} = 1\)

Answer 7

\[\large \int \limits_0^8 \sqrt[3]{x}~dx \approx \dfrac{1}{2}\left[f(1) + 2f(2) + \cdots + 2f(7) +f(8)\right]\]

Answer 8

you just need to evaluate the values and simplify @Lena772 ^

Answer 9

Thanks.. Do find the exact value i graph it?

Answer 10

To*

Answer 11

for exact value - as the question suggests, we have to evaluate the definite integral

Answer 12

you did the simpson's rule already ?

Answer 13

yes

Answer 14

Great ! use below formula for exact value :

\[\large \int x^n~dx = \dfrac{x^{n+1}}{n+1}+C\]

Answer 15

\[\large \int \limits_0^8 \sqrt[3]{x}~dx = \int \limits_0^8 x^{\frac{1}{3}}~dx = ? \]

Answer 16

43.3137

Answer 17

is what I got for Simpsons Rule

Answer 18

that doesn't look right

Answer 19

what about trapezoidal ?

Answer 20

I got 0 for trapezoidal :|

Answer 21

trapezoidal :
http://www.wolframalpha.com/input/?i=1%2F2%28%280%29%5E%281%2F3%29+%2B+2%281%29%5E%281%2F3%29+%2B+2%282%29%5E%281%2F3%29+%2B+2%283%29%5E%281%2F3%29+%2B+2%284%29%5E%281%2F3%29%2B+2%285%29%5E%281%2F3%29+%2B+2%286%29%5E%281%2F3%29++%2B+2%287%29%5E%281%2F3%29+%2B+%288%29%5E%281%2F3%29+%29

Answer 22

All the numbers are positive in the sum, there is no way for that to become a 0 - check your calculation once :)

Answer 23

ok ... i now get -45.1687 for simpsons rule

Answer 24

try again, there is no way for that sum to go negative...

Answer 25

simpsons :
http://www.wolframalpha.com/input/?i=1%2F3%28%280%29%5E%281%2F3%29+%2B+4%281%29%5E%281%2F3%29+%2B+2%282%29%5E%281%2F3%29+%2B+4%283%29%5E%281%2F3%29+%2B+2%284%29%5E%281%2F3%29+%2B+4%285%29%5E%281%2F3%29%2B2%286%29%5E%281%2F3%29+%2B+4%287%29%5E%281%2F3%29+%2B+8%5E%281%2F3%29+%29

Answer 26

I get 12 for exact value...

Answer 27

Is that right @ganeshie8