The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the G.P if its sum to infinity is 8.

Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)

Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.

Find the value of x for which the function y = x3 - x has a minimum value.

Find the volume of solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis.

What is the derivative of t2 sin (3t - 5) with respect to t?

Evaluate: \( \int_{0}^{z}(\sin x-\cos x)\,dx \) Where \( z=\frac{\pi}{4}.(\pi=pi) \)

Evaluate \( \int_{-2}^{1} (x - 1)^2 \, dx \)

The shaded portion in the graph is represented by