Question

Find the total mass of the wire with density ρ.

Answer 1

Step 1 :

The equation of the wire is and .

The wire density is .

Mass of the wire is.

Where .

Compare with .

and .

Substitute and in equation (1).

Substitute in .

Step 2 :

Find mass of wire :

Consider then .

Find the new limits:

when , .

when , .

Substitute the corresponding values in equation (2).

Mass of the wire is .

Solution :

Mass of the wire is .