simple integration artimethic errorI am trying to integrate a polynomial but I couldn't get the correct answer somehow. I feel like I'm making a mistake when evaluating the integral. π ∫ − 1 1 1 − 2 x 2 + x 4 d x = [ x − 2 x 3 3 + x 5 5 ] − 1 1 = 1 − 2 3 + 1 5 + 1 − 2 3 + 1 5 = 2 + 2 ( − 2 ) 3 + 2 ( 1 ) 5 = 30 − 26 15 = 4 15 πBut the integral calculator is giving me: 16 15 π

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simple integration artimethic errorI am trying to integrate a polynomial but I couldn&#039;t get the correct answer somehow. I feel like I&#039;m making a mistake when evaluating the integral.  π      ∫          −      1        1        1    −    2          x      2        +          x      4        d  x  =  [      x    −                            2                      x            3                          3              +                            x          5                5                  ]          −      1        1    =  1  −      2    3    +      1    5    +  1  −      2    3    +      1    5    =  2  +                    2        (        −        2        )            3        +                    2        (        1        )            5        =                    30        −        26            15        =      4    15    πBut the integral calculator is giving me:       16    15    π

vard6vv · Accepted Answer

(        x        −                  2          3                          x          3                +                  1          5                          x          5                )            |              −      1        1    =  1  −  (  −  1  )  −      2    3    (  1  −  (  −  1  )  )  +      1    5    (  1  −  (  −  1  )  )  =  =  2  −      4    3    +      2    5    =            30      −      20      +      6        15    =      16    15  You can avoid a lot of these problems in cases like this if you use the property      ∫          −      a        a    f  (  x  )  d  x  =  2      ∫    0    a    f  (  x  )  d  x    ,        a  &amp;gt;  0    ,      f  (  x  )      an even function,so in this case we&#039;d get  2      ∫    0    1    (  1  −  2      x    2    +      x    4    )  d  x  =  2            [      x      −              2        3                    x        3            +              1        5                    x        5            ]        0    1    =  =  2      (    1    −          2      3        +          1      5        )    =  2            15      −      10      +      3        15    =  2      8    15    =      16    15

simple integration artimethic error I am trying to integrate a polynomial but I couldn't get the c

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