A particle is fired straight up from the ground. Its height in feet after $t$ second is given by $s(t) = 128t - 16t^2$. The velocity of the particle when it hits the ground is...

The value of $c$ satisfied by the Rolle's theorem for the function $f(x) = x^2(1 - x)^2$, $x \in [0, 1]$ is...

The value of integral $\displaystyle\int \dfrac{dx}{\sin^2 x + \tan^2 x}$ is...

The value of integral $\displaystyle\int \dfrac{\sqrt{x^2 + 1}\,[\log(x^2 + 1) - 2\log x]}{x^4}\,dx$ is equal to...