Year 12 Maths - Specialist (Unit 3 & Unit 4)
Integral calculus
Arc length and surface area of revolution
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Question 1
197199
Which integral gives the arc length \(L\) of a smooth curve \(y=f(x)\) between \(x=a\) and \(x=b\)?
\(\displaystyle\int_a^b \sqrt{1+\left(\dfrac{dy}{dx}\right)^2}\,dx\)
\(\displaystyle\int_a^b \left(1+\dfrac{dy}{dx}\right)^2 dx\)
\(\displaystyle\int_a^b 2\pi y\sqrt{1+\left(\dfrac{dy}{dx}\right)^2}\,dx\)
\(\displaystyle\int_a^b \sqrt{1+\dfrac{dy}{dx}}\,dx\)
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