A spherical iron ball of $$10 \mathrm{~cm}$$ radius is coated with a layer of ice of uniform thickness that melts at the rate of $$50 \mathrm{~cm}^3 / \mathrm{min}$$. If the thickness of ice is $$5 \mathrm{~cm}$$, then the rate at which the thickness of ice decreases is

$$\int \frac{\sin \frac{5 x}{2}}{\sin \frac{x}{2}} d x=$$

(where $$C$$ is a constant of integration.)

The equation of the plane passing through the points $$(2,3,1),(4,-5,3)$$ and parallel to $$X$$-axis is

$$\text { If } \int e^{x^2} \cdot x^3 \mathrm{~d} x=e^{x^2} \cdot[f(x)+C]$$ (where $$C$$ is a constant of integration.) and $$f(1)=0$$, then value of $$f(2)$$ will be