I need help with this math problem.... It says set up the integral, but do not evaluate?

Question

A manufacturer needs to make corrugated metal sheets 36inches wide with cross sections in the shape of the curve

y = .5sinπx, 0≤x≤36

How wide must the original flat sheet be for the manufacturer to produce these corrugated sheets? Set up but do not evaluate the integral.

Answer 1

This is an arc-length problem.

You want the arc length of .5 sin(πx) from x=0 to x=36.

Just set up your integral based on the arc length integral:

∫ (a to b) √ ( 1 + (y' )²) dx

y' = .5π cos(πx)

∫ (0 to 36) √ ( 1 + (.5π cos(πx))²) dx

= ∫ (0 to 36) √ ( 1 + .25π cos²(πx)) dx

Answer 2

Sounds like a line integral problem. Look up that part of the course and see how to do it.