Primitives et intégrales - Q34 - 8. [Math] Problèmes mathématiques (niveau secondaire)

Primitives et intégrales - Q34

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

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Question 1:

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$\begin{equation*} \frac{d}{dx} \int_{1/x}^x \frac{dt}{t} \end{equation*}$

Format example : expression: 5x+3 equation: x=y+3 inequation: x<2y+1

Question 2:

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$\begin{equation*} \frac{d}{dx} \int_{\cos x}^{\sin x} \frac{dt}{1-t^2} \end{equation*}$

Format example : expression: 5x+3 equation: x=y+3 inequation: x<2y+1

Question 3:

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$\begin{equation*} \frac{d}{dx} \int_{-\sqrt{x}}^{2 \sqrt{x}} \sin (t^2) \, dt \end{equation*}$

Format example : expression: 5x+3 equation: x=y+3 inequation: x<2y+1

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

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