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Math Help - one of those "stupid" proofs

  1. #1
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    one of those "stupid" proofs

    Hi all, I have to do this problem according to the first part of the Fundamental Theorem of Calculus. Fundamental theorem of calculus - Wikipedia, the free encyclopedia

    h(x)= (integral of 0 to x^2) sqrt(1+r^3) dr

    answer:

    f(x)=sqrt(1+r^3)

    h'(x)=f(x)

    h'(x)=sqrt(1+x^6)* 2x


    Am I right? I was kind of confused, also did I miss any steps? Thanks!
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  2. #2
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    it's correct.
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  3. #3
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    Quote Originally Posted by soyeahiknow View Post
    Hi all, I have to do this problem according to the first part of the Fundamental Theorem of Calculus. Fundamental theorem of calculus - Wikipedia, the free encyclopedia

    h(x)= (integral of 0 to x^2) sqrt(1+r^3) dr

    answer:

    f(x)=sqrt(1+r^3)

    h'(x)=f(x)

    h'(x)=sqrt(1+x^6)* 2x


    Am I right? I was kind of confused, also did I miss any steps? Thanks!
    Dear soyeahiknow,

    Another approach is,

    h(x)=\int^{x^2}_{0}\sqrt{1+r^3}~dr

    Take y=x^2\Rightarrow{\frac{dy}{dx}=2x}

    \frac{d}{dy}h(x)=\frac{d}{dy}\int^{y}_{0}\sqrt{1+r  ^3}~dr

    \frac{d}{dx}h(x)\times{\frac{dx}{dy}}=\sqrt{1+y^3}

    h'(x)=\sqrt{1+y^3}\times\frac{dy}{dx}=\sqrt{1+x^6}  \times{2x}

    Hope this helps.
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