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VICSpecialist MathematicsQuick questions

Unit 4: Calculus

Quick questions on Volumes of revolution: VCE Specialist Mathematics Unit 4

6short 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 set up?
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Rotating about the xx-axis, use discs of radius y=x2y = x^2 and thickness dxdx, with xx from 00 to 22:
What is wrong variable for the axis?
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Rotating about the yy-axis means integrating πx2 dy\pi x^2\,dy in terms of yy, not πy2 dx\pi y^2\,dx.
What are mismatched limits?
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Use xx-limits when integrating in xx and yy-limits when integrating in yy.
What is q1?
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Write the disc-method volume for rotating y=f(x)y = f(x), a≤x≤ba \le x \le b, about the xx-axis. [1 mark]
What is q2?
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Find the volume when y=xy = \sqrt{x}, 0≤x≤40 \le x \le 4, is rotated about the xx-axis. [3 marks]
What is q3?
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State the washer integrand for outer radius R(x)R(x) and inner radius r(x)r(x). [1 mark]

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