Question

How do you do this question?

Answer 1

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