Volumes of Revolution (Edexcel A-Level Further Mathematics): Quizzes

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Volumes of Revolution
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What is the formula for volume when rotating around the x-axis?

V=πaby2dxV = \pi \int_a^b y^2 \, dx

Through what angle is the area rotated to form a volume of revolution?

360°360°

What is the formula for volume when rotating around the y-axis?

V=πabx2dyV = \pi \int_a^b x^2 \, dy

In the x-axis formula, what happens to yy before integration?

It is squared to give y2y^2

When rotating around the y-axis, what type of limits must be used?

y-limits

What is the first step when rotating around the y-axis?

Rearrange to get x=f(y)x = f(y)

The volume is approximated using what shape?

Discs

What important constant must not be forgotten in volume answers?

π\pi

How should irrational answers be presented?

In exact form

If y=x2y = x^2, what is y2y^2 for use in the x-axis volume formula?

x4x^4

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