If $\int_1^n [x] dx = 120$,then $n = $

If $f(t) = \int_{-t}^t \frac{e^{-|x|}}{2} dx$, then $\lim_{t \rightarrow \infty} f(t)$ is equal to:

$\int_0^1 {(1 - x)^9} dx = $

Let $a$ and $b$ be real constants such that the function $f$ defined by $f(x) = \begin{cases} x^2+3x+a, & x \leq 1 \\ bx+2, & x > 1 \end{cases}$ is differentiable on $\mathbb{R}$. Then,the value of $\int_{-2}^2 f(x) dx$ equals

If the value of the integral $\int_{0}^{1/2} \frac{x^{2}}{(1-x^{2})^{3/2}} dx$ is $\frac{k}{6}$,then $k$ is equal to

If $\int_a^b x^3 dx = 0$ and $\int_a^b x^2 dx = \frac{2}{3}$,then