Finding antiderivative problemsI'm having trouble understanding how to find these antiderivatives:1. e 2 Is the antiderivative just e 2 ⋅ x + c.2. f ( x ) = x 2 3 + x x = x 2 1 3 + x ⋅ x 1 2 = x 2 3 + x 3 2 So the antiderivative according to antiderivative formulas: A n t i = x 5 2 5 2 + x 5 2 5 2 = 2 ⋅ x 5 2 5 2 = 4 ⋅ x 5 2 5 + C = FIs this right?When I do a check, I don't get the original function: F ′ = 4 5 ⋅ 5 2 ⋅ x 3 2 = 2 ⋅ x 3 2 But that doesn't equal the original function. What did I do wrong?

Question

Finding antiderivative problemsI&#039;m having trouble understanding how to find these antiderivatives:1.       e    2  Is the antiderivative just       e    2    ⋅  x  +  c.2.   f  (  x  )  =            x      2        3    +  x      x    =      x                  2                              1            3                                +  x  ⋅      x                  1        2              =      x                  2        3              +      x                  3        2            So the antiderivative according to antiderivative formulas:  A  n  t  i  =            x                        5          2                            5      2        +            x                        5          2                            5      2        =  2  ⋅            x                        5          2                            5      2        =  4  ⋅            x                        5          2                      5    +  C  =  FIs this right?When I do a check, I don&#039;t get the original function:      F    ′    =      4    5    ⋅      5    2    ⋅      x                  3        2              =  2  ⋅      x                  3        2            But that doesn&#039;t equal the original function. What did I do wrong?

benedictazk · Accepted Answer

Explanation:1. It is correctYou are making a calculation mistake (considering       2    3   as       3    2  ) Otherwise all other things are correct

preityk7t · Accepted Answer

Step 11. Correct, because       e    2   is just a constant, and for any constant function   f  (  x  )  =  a, the antiderivative is   a  x  +  C.Step 2Note that       3    2    ≠      2    3  , and one becomes       5    2   the other one becomes       5    3  , so the correct antiderivative is       2    5        x                  5        2              +      3    5        x                  5        3              +  C

Finding antiderivative problems I'm having trouble understanding how to find these antiderivatives:

Answered question

Answer & Explanation

New Questions in Calculus 1