00:01
In this question we are asked to find the line integration of the vector field f along the path rt from point 1 .0 .1 to 0 .8 to the power 2 pi.
00:13
So let's start to solve this problem.
00:15
We know line integration of f vector along the path r vector is given by f vector.
00:25
F vector dot dr vector.
00:28
And here f vector is equal to x square i plus y square j plus z square k and we know d r vector is equal to d x i plus d y z z k now from this we obtain line integration of f factor is equal to x i plus d y z k.
01:01
Y square d y plus z square d z suppose this is equation number one here we have r t vector is equal to cos t i plus sine t z z plus into the power t k and we know r t vector is given by x i plus y z plus z k and this is equal to cos t i plus sine t j j plus e to the power t k now by comparing the coefficients of i j and k we obtain x is equal to cos t y equals to sine t and z equals to e to the power t now after differentiating these three with respect to t we 10, dx is equal to negative, sine t d t, d t, d, d, y is equal to, kosti, d, d t, and d z is equal to u to the power t, d t.
02:11
Now here we are moving along this path from this point to this point.
02:18
Now next we will find the range of t when we are moving from this point to this point.
02:27
You can pick any of three from x, y and z to find the range of t.
02:32
Here i pick z equals to e to the power t to find the range of t.
02:38
Here when z equals to one, then we obtain t equals to zero...