MCQ
$\int_0^1 {\frac{{{{\tan }^{ - 1}}x}}{{1 + {x^2}}}} \,dx = $
- A$\frac{{{\pi ^2}}}{8}$
- B$\frac{{{\pi ^2}}}{{16}}$
- C$\frac{{{\pi ^2}}}{4}$
- ✓$\frac{{{\pi ^2}}}{{32}}$
$\Rightarrow dt = \frac{1}{{1 + {x^2}}}dx,$ then
$\int_0^1 {\frac{{{{\tan }^{ - 1}}x}}{{1 + {x^2}}}dx = \int_0^{\pi /4} {t\,dt = \left[ {\frac{{{t^2}}}{2}} \right]_0^{\pi /4} = \frac{{{\pi ^2}}}{{32}}} } $.
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where $‘c’$ is constant of integration .
$\begin{array}{|l|l|l|l|l|l|} \hline X=x & 0 & 1 & 2 & 3 & 4 \\ \hline P(X=x) & \frac{1}{3} & \frac{1}{2} & 0 & \frac{1}{6} & 0 \\ \hline \end{array}$
, then
Three persons, A, B and C, fire at a target in turn, starting with A. Their probability
of hitting the target are 0.4, 0.3 and 0.2 respectively. The probability of two hits
is: