Question

A particle moves along the curve 6y = x³ + 2. Find the points on the curve at which y-coordinate is changing 2 times as fast as x-coordinate.

Find : $\textstyle\int$$\left({\frac{1-x}{1+x^{2}}}\right)^{2}e^{x}d x~.$

Find the general solution of the differential equation ${\frac{d y}{d x}}+2y=e^{3x}$

if $|\stackrel{\rightarrow}{a}+\stackrel{\rightarrow}{b}|$ =60, $|\stackrel{\rightarrow}{a}-\stackrel{\rightarrow}{b}|$=40 and $\stackrel{\rightarrow}{a}\$=22,then find $\stackrel{\rightarrow}{b}\$.

The radius r of a right circular cylinder is decreasing at the rate of 3 cm/min. and its height h is increasing at the rate of 2 cm/min. When r =7 cm and h = 2 cm, find the rate of change of the volume of cylinder. $[\mathrm{Use}\:\pi=\:\frac{22}{7}\:]$

The volume of a cube is increasing at the rate of 9 cm³/sec. How fast is the surface area increasing when the length of an edge is 10 cm.

Find : $\textstyle\int$$\frac{d x}{5-8\,x-x^{2}}$