← Integration methods: past papers
AS 91579 · 2024 paper · expansion, constants, DE, mass
Question 2(a) Achieved
Practises Standard integrals
Expand-then-integrate, a lower limit recovered from a definite integral, a separable equation in y², an area between a curve and a horizontal line, and a physical integral left entirely in symbols.
Find int (3x4 + 4)2 dx.
Work it out
Try it on paper first. Stuck? Take one hint at a time.
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1 The inside of the bracket is not linear, so the reverse chain rule will not work. What will?
Expand the square first: (3x4 + 4)2 = 9x8 + 24x4 + 16. -
2 Integrate term by term.
int (9x8 + 24x4 + 16)dx = x9 + 24x5/5 + 16x + 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.