The equation of a curve is such that dy/dx = kx³ + 2/x², where k is a constant. The curve passes through the point S (2, 20) and the gradient of the curve at S is 65/2.

Show that ∫₁⁴ x^(-1/2) ln x dx = 2 – ln 4.

It is given that ∫⁽³ᵃ⁾ₐ (2/(2x-5)) dx = ln(7/2). Find the value of the positive constant a.

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

Richard has 3 blue candles, 2 red candles and 6 green candles. The candles are identical apart from their colours. He…

In Greenton, 70% of the adults own a car. A random sample of 8 adults from Greenton is chosen.

The booklets produced by a certain publisher contain, on average, 1 incorrect letter per 30 000 letters, and these er…