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andreea567
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Pe: 2020-12-01T19:58:54+02:00 In: In:

Ma puteti ajuta va rog cu acest …

Ma puteti ajuta va rog cu acest ex?

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  1. Menim
    Best Answer

    Putem simplifica integrala facand substitutia y=2x+1. Derivand, obtinem ca dy=2dx, sau altfel spus \frac12 dy=dx.
    Atunci cand x=1, y=2*1+1=3, si atunci cand x=2, y=2*2+1=5.
    Integrala devine:
    \frac12\int_3^5\frac1{x^3}dx=\frac12\int_3^5x^{-3}dx=\frac12\frac{x^{-3+1}}{-3+1}|_3^5=\frac12\frac{x^{-2}}{-2}|_3^5=-\frac{1}{4}\frac1{x^2}|_3^5=-\frac14(\frac1{25}-\frac1{9})
    Poti continua calculele daca doresti(aducere la acelasi numitor etc.).

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