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EEMajor12

  • 2 years ago

Integral Question

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  1. EEMajor12
    • 2 years ago
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    f(x)=\int_1^{3x^5} \ln(t^2+1) \, dt

  2. satellite73
    • 2 years ago
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    \[f(x)=\int_1^{3x^5} \ln(t^2+1) \, dt\]like that?

  3. satellite73
    • 2 years ago
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    is the question find the derivative?

  4. EEMajor12
    • 2 years ago
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    yes it is,

  5. satellite73
    • 2 years ago
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    how'd i guess?

  6. imranmeah91
    • 2 years ago
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    too hard to integrate

  7. satellite73
    • 2 years ago
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    use the chain rule. the derivative of the integral is the integrand, so replace t by \[3x^5\] and then multiply the answer by \[15x^4\]

  8. EEMajor12
    • 2 years ago
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    yeah im having trouble with these. Ill try it sat!

  9. satellite73
    • 2 years ago
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    \[f'(x)=\ln((3x^5)^2+1)\times 15x^4\]

  10. satellite73
    • 2 years ago
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    i should have let you do it on your own, but once you see it you should realize how easy it is. it is clear what i did yes?

  11. satellite73
    • 2 years ago
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    if you need a word of explanation let me know

  12. EEMajor12
    • 2 years ago
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    i understand chain rule for ln (function within function). where did the 15x4 come from?

  13. EEMajor12
    • 2 years ago
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    nvm 3x^5 derivative

  14. EEMajor12
    • 2 years ago
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    15x^4 \ln(9x^{10}+1) ?

  15. satellite73
    • 2 years ago
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    yes

  16. satellite73
    • 2 years ago
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    it is the chain rule and you have a composite function. don't forget that \[F(x)=\int_a^x f(t)dt\] is a function of "x" so if you do not have an x in the upper limit, but rather something else, you have a composition like \[F(g(x))=\int_a^{g(x)}f(t)dt\] and so you need the chain rule

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