EDB β€” 1B0

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Exercises

  1. [1B0]Prerequisites:Fundamental theorem of integral calculus.

    Suppose that \(f:[a,b]→ℝ\) is continuous and \(g:ℝ→ℝ\) has class \(C^ 1\): prove that

    \[ ∫_ a^ b f(g(t)) g'(t) \, {\mathbb {d}}t = ∫_{g(a)}^{g(b)} f(s) \, {\mathbb {d}}s \quad . \]

    Solution 1

    [1B2]

    Note that for this result it is not necessary to assume that \(g\) is monotonic.

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