Use the substitution 2x = tan θ to find the exact value of ∫(from 0 to 1/2) 12 / (1+4x²)² dx. Give your answer in the form a+bπ, where a and b are rational numbers.

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.

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…

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…

Lengths of a certain species of lizard are known to be normally distributed with standard deviation 3.2 cm. A natural…