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Kamille

  • one year ago

Hello, can anyone help me? \[\int\limits_{2}^{8}\sqrt({2x})dx=\sqrt{2}\int\limits_{2}^{8}(x ^{\frac{ 1 }{ 2 }})dx=\sqrt{2}(\frac{ x ^{1,5} }{ 1,5})\] so, my questions are "Have I done everything right" And "How to find the answer?". p.s. there, of course, should be | with 8 on top of it and 2 on the bottom, but I didnt know how to "draw it"

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  1. TuringTest
    • one year ago
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    yes, it's right so far

  2. Kamille
    • one year ago
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    so, I know that I need to "put" 8 and 2 everywhere where is x, but! how to simplify (or I don't need to) \[\frac{ 8^{1,5} }{ 1,5 }\]

  3. TuringTest
    • one year ago
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    it helps to remember that\[\large x^{a/b}=\sqrt[b]{x^a}\]and convert 1.5=3/2

  4. Kamille
    • one year ago
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    \[\sqrt{2}(\frac{ \sqrt{8^{3}} }{ 1,5 }-\frac{ \sqrt{8} }{ 1,5 })=\sqrt{2}(\frac{ 8\sqrt{8} }{ 1,5 }-\frac{ \sqrt{8} }{ 1,5 })=\sqrt{2} * \frac{ 7\sqrt{8} }{ 1,5 }= 18\frac{ 2 }{ 3 }\] Can you check now? @TuringTest

  5. TuringTest
    • one year ago
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    yes, that is correct for the evaluation at 8, now you need to subtract the evaluation at 2

  6. Kamille
    • one year ago
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    sorry? Haven't i done it? \[2^{\frac{ 3 }{ 2 }}=\sqrt{8}\]

  7. TuringTest
    • one year ago
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    yeah, my bad, I got cut off you have the right answer

  8. Kamille
    • one year ago
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    Thank you a lot for your help!

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