Quick questions on Integration by substitution in HSC Maths Extension 1: choosing $u$ , transforming the integral and changing limits

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is changing limits, stage by stage?

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The mechanics that students most often slip on is the definite integral: choosing

u

, transforming the differential, and changing the limits in step. The figures below walk through the 2022 HSC integral

\displaystyle\int_0^1 x\sqrt{x^2+3}\,dx

to show how the substitution moves the whole problem from

x

-space to

u

-space while preserving the area.

What are reverse chain rule patterns?

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Memorise these common patterns; recognising them on sight saves setting up a full substitution:

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