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VICSpecialist MathematicsQuick questions

Unit 4: Calculus

Quick questions on Arc length and surface area: VCE Specialist Mathematics Unit 4

5short 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 wrong radius for the surface?
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Rotation about the xx-axis uses radius yy (factor 2πy2\pi y); about the yy-axis uses radius xx.
What are mismatched limits?
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In parametric problems integrate over tt with tt-limits, not xx-limits.
What is q1?
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Write the Cartesian arc-length integral for y=f(x)y = f(x) from aa to bb. [1 mark]
What is q2?
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Set up the parametric arc-length integral for x=cos⁡tx = \cos t, y=sin⁡ty = \sin t, 0≤t≤π0 \le t \le \pi. [2 marks]
What is q3?
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State the surface-area integrand for rotating y=f(x)y = f(x) about the xx-axis. [1 mark]

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