exo7 4351

Construire les courbes représentatives des fonctions suivantes :

1

\(f(x) = \int_{t=-\pi/2}^{\pi/2} |x+t|\sin t\,d t\).

2

\(f(x) = \int_{t=x}^{x^2} \frac{d t}{\ln t}\).

3

\(f(x) = \int_{t=x}^{x^2} \frac{d t}{\sqrt{t^4+t^2+1}}\).

4

\(f(x) = \int_{t=0}^1 \frac{e^t\,d t}{t+x}\).

5

\(f(x) = \int_{t=0}^{\pi/2} x\exp\Bigl(\frac{\sin t}x\Bigr)d t\).

6

\(f(x) = \int_{t=0}^x \frac{\ln(1+xt)}{1+t^2}\,d t\).