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sarathkothapalli Group Title

Integral of (x^3.^root(4x-x^2) dx with integral limits 0,4 Integral of x^4/(1+x^2)^4 dx with integral limits 0,5 pls giv me solution for above 2 questns in detailled steps

  • 2 years ago
  • 2 years ago

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  1. Mimi_x3 Group Title
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    \[\int x^{3}\sqrt{x^{2}-4} dx\]

    • 2 years ago
  2. Mimi_x3 Group Title
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    Is that the integral?

    • 2 years ago
  3. Mimi_x3 Group Title
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    I mean: \[\large \int\limits x^{3}\sqrt{4x-x^{2}} dx\]?

    • 2 years ago
  4. sarathkothapalli Group Title
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    Yes limits given in questn

    • 2 years ago
  5. sarathkothapalli Group Title
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    Pls giv me slution in steps as i need to note it

    • 2 years ago
  6. lgbasallote Group Title
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    i think you're supposed to do completing the swuare here

    • 2 years ago
  7. Mimi_x3 Group Title
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    well, it's completing the square first then trig-sub. Why not you try it; then me typing the solution for you?

    • 2 years ago
  8. Mimi_x3 Group Title
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    than me*

    • 2 years ago
  9. sarathkothapalli Group Title
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    I dont know how to do,pls giv me steps

    • 2 years ago
  10. exraven Group Title
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    \[4x - x^2 = -(x^2 - 4x)\]\[= -(x^2 - 4x) - 4 + 4\]\[= -(x^2 - 4x + 4) + 4\]\[= 4 - (x^2 - 4x + 4)\]\[= 4 - (x - 2)^2\]\[\int\limits x^3 \sqrt{4x - x^2}dx = \int\limits x^3 \sqrt{4 - (x - 2)^2} dx\]there i already completed the square for you, just do trig subs and you'll be fine

    • 2 years ago
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