The problems in Exercises, are called self-answering problems because the answers are embedded in the question. For example, how many ways can you arrange the letters in the word “six”? The answer is six.

At time t = 0, water begins pouring into an empty tank so that the volume of water is changing at a rate V′(t) = sec²t. For time t = k, where 0 ≤ k ≤ π/2, determine the amount of water in the tank.