Answer:
The value of [tex]\int _C\bigtriangledown f\cdot dr[/tex] is 40.
Step-by-step explanation:
It is given that the gradient of function is continuous.
By fundamental theorem for line integrals,
[tex]\int _C\bigtriangledown f\cdot dr=f(Q)-f(P)[/tex]
Where, C starts from P and end at the point Q.
We have to find the value of [tex]\int _C\bigtriangledown f\cdot dr[/tex].
The function is defined from contour line 10 to contour line 50.
[tex]\int _C\bigtriangledown f\cdot dr=50-10[/tex]
[tex]\int _C\bigtriangledown f\cdot dr=40[/tex]
Therefore the value of [tex]\int _C\bigtriangledown f\cdot dr[/tex] is 40.
