Answer:
∫₂³ √(1 + 64y²) dy
Step-by-step explanation:
∫ₐᵇ f(y) dy is an integral with respect to y, so the limits of integration are going to be the y coordinates. a = 2 and b = 3.
Arc length ds is:
ds = √(1 + (dy/dx)²) dx
ds = √(1 + (dx/dy)²) dy
Since we want the integral to be in terms of dy, we need to use the second one.
ds = √(1 + (8y)²) dy
ds = √(1 + 64y²) dy
Therefore, the arc length is:
∫₂³ √(1 + 64y²) dy
