# approximate the integral Simpson's Rule & trapezoidal rule

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• Aug 28th 2006, 03:28 PM
Yogi_Bear_79
approximate the integral Simpson's Rule & trapezoidal rule
As always your help is greatly appriciated!

Approximate the integral $\displaystyle \int_{0}^{1}x^4dx ; n =6$, by

a.) first applying Simpson's Rule and
b.) then applying the trapezoidal rule
• Aug 28th 2006, 04:28 PM
ThePerfectHacker
Quote:

Originally Posted by Yogi_Bear_79
As always your help is greatly appriciated!

Approximate the integral $\displaystyle \int_{0}^{1}x^4dx ; n =6$, by

a.) first applying Simpson's Rule and

The arithmetic I am not going to do.
Since $\displaystyle n$ is even so you can apply Simpons rule.
$\displaystyle \int_0^1 x^4 dx\approx$$\displaystyle \frac{1}{3}\big( (0)^4+4(1/6)^4+2(2/6)^4+$$\displaystyle 4(3/6)^4+2(4/6)^4+4(5/6)^4+(6/6)^4 \big) \frac{1}{6}$
• Aug 31st 2006, 08:55 AM
Yogi_Bear_79
Thanks for your help. Can anyone help with the trapezoidal rule section of the problem?
• Aug 31st 2006, 09:08 AM
ThePerfectHacker
Quote:

Originally Posted by Yogi_Bear_79
Thanks for your help. Can anyone help with the trapezoidal rule section of the problem?

Same idea.
$\displaystyle \frac{1}{2}\big( 0^4+2(1/6)^4+2(2/6)^4+2(3/6)^4$$\displaystyle +2(4/6)^4+2(5/6)^4+(6/6)^4 \big)\cdot \frac{1}{6}$