← MATH 01131 · Calculus II
MATH 01131 · Applications
Arc length / surface area ideas
Definition
Arc length L=∫ₐᵇ √(1+(y′)²) dx. Surface of revolution: S=2π∫ radius · √(1+(y′)²) dx (radius = distance to axis).
Read this
These integrals are often messy — setup skill matters more than closed forms.
Parametric versions replace with √((dx/dt)²+(dy/dt)²) dt.
Check that the derivative exists and is continuous on the interval.
Drill with flashcards
Flip through these until you can say the answer before revealing it.
Flashcards · 1 / 3
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Try this
Attempt each problem first, then open the worked solution.
1.Set up arc length of y=x^{3/2} from 0 to 4 (do not force a pretty answer).