Question 2(a) Achieved

An exponential integral, a negative-power differential equation, an upper limit that appears on both sides, a trig quotient whose top is a multiple of the derivative of its bottom, and a proportional-to-the-square model built from scratch.

Find int 4e^{2x − 1} dx.

The 2023 paper, page 6 ↗ Marking schedule, page 3 ↗

Work it out

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

1. 1 What does e^{2x − 1} integrate to?

   Itself, divided by the 2 in front of x: (1/2) e^{2x − 1}.

2. 2 Bring in the 4.

   int 4e^{2x − 1} dx = 4 × (1/2) e^{2x − 1} + c = 2e^{2x − 1} + 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 2023 marking schedule.

How did it go?

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