Question 3(a) Achieved

Two exponential terms to integrate, a log-form differential equation, an upper limit that appears on both sides, a bisected cosine area, and Newton’s law of cooling built from scratch.

Find int (e^2x + 3/e^4x)dx.

The 2024 paper, page 10 ↗ Marking schedule, page 5 ↗

Work it out

Try it on paper first. Stuck? Take one hint at a time.

1. 1 Bring e^4x up from the bottom.

   3/e^4x = 3e^−4x

2. 2 Integrate each exponential: divide by the number in front of x.

   int (e^2x + 3e^−4x)dx = (1/2) e^2x + 3e^−4x/(−4) + c = (1/2) e^2x − (3/4) e^−4x + c

What the marker wanted

• Achieved The correct integral. The schedule says the + c is not required for it.

In our words, from NZQA’s 2024 marking schedule.

How did it go?

Got it moves it further out. Review brings it back tomorrow.