A particle starts from origin with a velocity (in m/s) given by the equation $\rm \frac{dx}{dt}=x+1$. The time (in seconds) taken by the particle to traverse a distance of 24 m is:

What is $\rm \int_0^a \frac{f(a-x)}{f(x)+f(a-x)}\ dx $ equal to?

What is $\rm\mathop {\lim }\limits_{x \to 2}\frac{x^3 + x^2}{x^2 + 3x + 2}$ equal to?

If $\rm \int_0^a \left[f(x)+f(-x)\right]dx=\int_{-a}^{\ \ a} g(x)\ dx $, then what is g(x) equal to?