Evaluate ∫ − 1 0 ( x 4 − x 2 + 2 ) d x using Simpson's Rule

Question

Evaluate       ∫          −      1              0        (      x    4    −      x    2    +  2  )  d  x using Simpson&#039;s Rule

Arianna Turner · Accepted Answer

Simpson&#039;s Rule states  Q  (  f  )  =            b      −      a        6    (  f  (  a  )  +  4  f  (            a      +      b        2    )  +  f  (  b  )  )In our case:  a  =  −  1  ,  b  =  0  Q  (  f  )  =            0      −      (      −      1      )        6    (  f  (  −  1  )  +  4  f  (            −      1      +      0        2    )  +  f  (  0  )  )      1    6    (  2  +  4      29    32    +  2  )  =      2    3    (  1  +      29    16    )  =      15    8    =  1.875If we evaluate the integral directly, we get      28    15    ≈  1.8667We thus see that our result is &quot;very&quot; close to the exact value.

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