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Math Help - Funtions and Primitives

  1. #1
    mei
    mei is offline
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    Funtions and Primitives

    Hey there!
    I was given the following exercise:

    The function h:\mathbb{R} \longrightarrow \mathbb{R} is consistent with the following:
    h'(x)=(3x-2)\sqrt{1+|2x|}

    and

     h(1)=0.

    Calculate h(-1).

    So I have tried to calculate the primitive of the function h'(x) so I could get to h(x) but everything I've tried calculating doesn't give me h(1)=0. Even inputing h'(x) into Wolfram Integrator gives me a certain h(x) that doesn't comply with h(1)=0.

    Could you please have a look at it and let me know how you'd do it?
    Thanks in advance!
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  2. #2
    Super Member malaygoel's Avatar
    Joined
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    Quote Originally Posted by mei View Post
    Hey there!
    I was given the following exercise:

    The function h:\mathbb{R} \longrightarrow \mathbb{R} is consistent with the following:
    h'(x)=(3x-2)\sqrt{1+|2x|}

    and

     h(1)=0.

    Calculate h(-1).

    So I have tried to calculate the primitive of the function h'(x) so I could get to h(x) but everything I've tried calculating doesn't give me h(1)=0. Even inputing h'(x) into Wolfram Integrator gives me a certain h(x) that doesn't comply with h(1)=0.

    Could you please have a look at it and let me know how you'd do it?
    Thanks in advance!
    You will be getting some h(x), and hence some h(1). Suppose you are getting h(1)=4

    then change your h(x) like this
    your new h(x) will be h(x)-4
    See that h(x) and h(x)-4 have the same h'(x)
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