$$\int\limits_0^\pi {xf\left( {\sin x} \right)dx} $$ is equal to

$$\int\limits_{ - {{3\pi } \over 2}}^{ - {\pi \over 2}} {\left[ {{{\left( {x + \pi } \right)}^3} + {{\cos }^2}\left( {x + 3\pi } \right)} \right]} dx$$ is equal to

The differential equation whose solution is $$A{x^2} + B{y^2} = 1$$
where $$A$$ and $$B$$ are arbitrary constants is of

At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of $$5$$ phone calls during $$10$$ minute time intervals. The probability that there is at the most one phone call during a $$10$$-minute time period is :