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Math Help - approximate the integral Simpson's Rule & trapezoidal rule

  1. #1
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    approximate the integral Simpson's Rule & trapezoidal rule

    As always your help is greatly appriciated!

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

    a.) first applying Simpson's Rule and
    b.) then applying the trapezoidal rule
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  2. #2
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    Quote Originally Posted by Yogi_Bear_79
    As always your help is greatly appriciated!

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

    a.) first applying Simpson's Rule and
    The arithmetic I am not going to do.
    Since n is even so you can apply Simpons rule.
    \int_0^1 x^4 dx\approx  \frac{1}{3}\big( (0)^4+4(1/6)^4+2(2/6)^4+ 4(3/6)^4+2(4/6)^4+4(5/6)^4+(6/6)^4 \big) \frac{1}{6}
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  3. #3
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    Thanks for your help. Can anyone help with the trapezoidal rule section of the problem?
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  4. #4
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    Quote Originally Posted by Yogi_Bear_79
    Thanks for your help. Can anyone help with the trapezoidal rule section of the problem?
    Same idea.
    \frac{1}{2}\big( 0^4+2(1/6)^4+2(2/6)^4+2(3/6)^4 +2(4/6)^4+2(5/6)^4+(6/6)^4 \big)\cdot \frac{1}{6}
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