Computing ∫ 0 1 1 + 3 x + 5 x 3 x d xMy idea for this was to break each numerator into its own fraction as follows ∫ 0 1 ( 1 x + 3 x x + 5 x 3 x ) d x ∫ 0 1 ( x − 1 / 2 + 3 x 1 / 2 + 5 x 5 / 2 ) d x ∫ 0 1 2 x 1 / 2 + 2 x 3 / 2 + 10 7 x 7 / 2 Not really sure where to go from there. Should I sub 1 in for the x values and let that be the answer?

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Computing       ∫    0    1              1      +      3      x      +      5              x        3                    x           d  xMy idea for this was to break each numerator into its own fraction as follows      ∫    0    1        (          1              x              +                  3        x                    x              +                  5                  x          3                            x              )    d  x      ∫    0    1    (      x          −      1              /            2        +  3      x          1              /            2        +  5      x          5              /            2        )     d  x      ∫    0    1    2      x          1              /            2        +  2      x          3              /            2        +      10    7        x          7              /            2      Not really sure where to go from there. Should I sub 1 in for the x values and let that be the answer?

Pasrbekwp · Accepted Answer

It looks like you&#039;ve already done the integration correctly, but forgot to take off the integration sign. The last line should be            [      2              x                  1                      /                    2                    +      2              x                  3                      /                    2                    +              10        7                    x                  7                      /                    2                    ]        0    1  which you can evaluate by substituting   x  =  1 and   x  =  0, and subtracting.You asked whether you should substitute   x  =  1: this will happen to give you the right answer, but only coincidentally, because the expression becomes   0 when   x  =  0

Marco Hudson · Accepted Answer

Hint: the formula  ∫      x    c      d  x  =            x              c        +        1                    c      +      1        +  Capplies to all real numbers   c  ≠  −  1, not just integers.

Computing int_0^1 (1+3x+5x^3)/(sqrt(x))\ dx

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