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Author(s) Philippe Delsarte, Manon Oreins
Deadline No deadline
Submission limit No limitation
Category tags Int

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Primitives et intégrales - Q34

Calculer les expression suivantes en appliquant le théorème de Leibniz selon lequel \(\frac{d}{dx} \int_{a(x)}^{b(x)} f(t) \, dt = b'(x) \cdot f(b(x)) - a'(x) \cdot f(a(x))\).

Question 1:
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\begin{equation*} \frac{d}{dx} \int_{1/x}^x \frac{dt}{t} \end{equation*}
Question 2:
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\begin{equation*} \frac{d}{dx} \int_{\cos x}^{\sin x} \frac{dt}{1-t^2} \end{equation*}
Question 3:
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\begin{equation*} \frac{d}{dx} \int_{-\sqrt{x}}^{2 \sqrt{x}} \sin (t^2) \, dt \end{equation*}