Question

Evaluate the line integral, where C is the given curve.

C is the right half of the circle x2 + y2 = 16

Answer 1

Step 1:

The integral is and is the right half of the circle.

Definition of the line integral :

If F is a continuous vector field on a smooth curve C, the function in the interval .

Then the line integral of F on C  is .

The unit circle can be parameterized of the equation are and .

Since the right half of the circle, integrate the function in the interval .

Then .

Step 2:

The line integral of is

Consider .

Then the limits of integration will change from to

Substitute and in the above integral.

            

Solution :

.