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