Evaluate the line integral, where C is the given curve. Integral C x \sin

Jaya Legge 2021-10-07 Answered
Evaluate the line integral, where C is the given curve. Integral C x sin y ds, C is the line segment from (0, 3) to (4, 6)
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Expert Answer

bahaistag
Answered 2021-10-08 Author has 101 answers
Recall the way we parametrize the segment between the two points. First, find the vector determined by the given two points:
(4,6)-(0,3)=(4,3)
The starting point is (0,3). The segment can be now parametrized as:
γ(t)=(0,3)+(4t,3t)=(4t,3t+3),t[0,1]
Next, find the derivative of the parametrization.
γ(t)=(4,3)||γ(t)||=42+32=5
Finally, we calculate the integral:
014tsin(3+3t)5dt=2001tsin(3+3t)dt=20sin660cos620sin39
Result:
20sin660cos620sin39
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