LU1MA001

\(\int _{0}^1 t\cos (t)dt=\)

1. \(-\sin (t).t^2\)

2. \(t.\cos (t)-\sin (t)\)

3. \(t.\sin (t)+\cos (t)\)

4. \(-\cos (1)-\sin (1)-1\)

5. \(\cos (1)+\sin (1)-1\)

Une primitive de \(\frac{1}{1+x^2}\) est

1. \(\ln (1+x^2)\)

2. \((1+x^2)^{1/2}\)

3. \(\frac{1}{1+x^3}\)

4. \(\arcsin (x)\)

5. \(\arctan (x)\)

\(\int _{\frac{\pi ^2}{4}}^{\pi ^2} \frac{\sin (\sqrt{x})}{\sqrt{x}}=\)

1. 0

2. \(-1\)

3. \(-2\)

4. 1

5. 2

\(\int _{0}^{1} \frac{4x+2}{x^2+x+1}=\)

1. 0

2. \(2\)

3. \(\ln (2)\)

4. \(3\ln (2)\)

5. \(2\ln (3)\)

Une primitive de \(\sin (x).\sqrt{\cos (x)}\) est

1. \(\log (\cos (x))\)

2. \(\frac{1}{\cos (x)}\)

3. \(\frac{1}{3}\cos (x)^\frac {1}{2}\)

4. \(\frac{1}{3}\sin (x)^\frac {1}{2}\)

5. \(\frac{-2}{3}\cos (x)^\frac {3}{2}\)

\(\mathrm{lim}_{x\to 0}\, \frac{x}{2+\sin (\frac{1}{x})}=\)

1. \(+\infty \)

2. \(\frac{1}{2}\)

3. \(0\)

4. n’existe pas.

5. \(-1\)