Question

Use a line integral on the boundary to find the area of the following region.

a disk of radius 2 .
set up the integral needed to find the area using the standard parameterization for a circle. use t as the independent variable.
__
∫ (__) dt
0

Answer 1

To find the area of a disk of radius 2 using a line integral on the boundary, we can parameterize the circle using the standard parameterization for a circle and set up the integral. The line integral to find the area is given by ∫ 2pi*r*sqrt((dx/dt)² + (dy/dt)²) dt, where r is the radius of the disk and t ranges from 0 to 2*pi.

Step-by-step explanation:

To find the area of a disk of radius 2 using a line integral on the boundary, we can parameterize the circle using the standard parameterization for a circle. Let the independent variable be t. The equation of a circle with radius r centered at the origin can be parameterized as x = r*cos(t), y = r*sin(t), where t ranges from 0 to 2*pi. The line integral to find the area is given by:

∫ 2pi*r*sqrt((dx/dt)² + (dy/dt)²) dt, where r is the radius of the disk and t ranges from 0 to 2*pi.