Mon p'tit WebCAM

Déterminez si l'intégrale donnée est convergente ou divergente. Si elle converge, donnez-en la valeur.

1. \(\displaystyle \int_0^{+\infty}\frac{1}{1+x^2}\,dx\)

2. \(\displaystyle \int_2^5\frac{1}{\sqrt{t-2}}\,dt\)

3. \(\displaystyle \int_0^4\frac{1}{x^2-4}\,dx\)

4. \(\displaystyle \int_7^{+\infty}\frac{1}{x^2-5x+6}\,dx\)

5. \(\displaystyle \int_0^7\frac{1}{x^2-5x+6}\,dx\)

6. \(\displaystyle \int_0^{\pi/2}\sec\theta\,d\theta\)

7. \(\displaystyle \int_0^1\ln x\,dx\)

8. \(\displaystyle \int_1^{+\infty}\frac{e^{-\sqrt{x}}}{\sqrt{x}}\,dx\)

9. \(\displaystyle \int_1^{+\infty}\frac{\ln x}{x}\,dx\)

10. \(\displaystyle \int_0^5\frac{y}{y-2}\,dy\)