The diagram shows part of the curve y = a/x, where a is a positive constant. Given that the volume obtained when the shaded region is rotated through 360° about the x-axis is 24π, find the value of a.

Find ∫(π/3 to π/6) x sec²x dx. Give your answer in a simplified exact form.

A curve is such that dy 6 = and A (1, -3) lies on the curve. A point is moving along the curve dx (3x-2)3 and at A th…

Express 5√3 cos x + 5 sin x in the form R cos(x – α), where R > 0 and 0 < α < ½π.

The sequence of values given by the iterative formula x_n+1 = (2x_n^6 + 12x_n) / (3x_n^5 + 8) with initial value x₁ =…

Given that sin(θ + 45°) + 2 cos(θ + 60°) = 3 cos θ, find the exact value of tan θ in a form involving surds. You need…

The variables x and y satisfy the relation sin y = tan x, where –½π < y < ½π. Show that dy/dx = 1 / (cos x √(cos 2x)).