Question

Find the length of the arc of the curve from point P to point Q.

Answer 1

Step 1:

The parabola equation is .

Differentiate each side with respect to x.

Use the power rule of derivative:

Hence, .

Step 2:

Find the length of the curve from  .

The formula for arc length is 

Substitute in above formula.

Use the property : .

The length of the arc is .

Solution :

The length of the arc from P to Q is .