The value of

$$\sum\limits_{n = 1}^{10} {} \int\limits_{ - 2n - 1}^{ - 2n} {{{\sin }^{27}}} x\,dx + \sum\limits_{n = 1}^{10} {} \int\limits_{2n}^{2n + 1} {{{\sin }^{27}}} x\,dx$$ is equal to

$$\int\limits_0^2 {[{x^2}]} \,dx$$ is equal to

Let f, be a continuous function in [0, 1], then $$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{j = 0}^n {{1 \over n}} f\left( {{j \over n}} \right)$$ is

The value of the integration

$$\int\limits_{ - {\pi \over 4}}^{\pi /4} {\left( {\lambda |\sin x| + {{\mu \sin x} \over {1 + \cos x}} + \gamma } \right)} dx$$