PG entrance exam CUET PG 2025 Mock Test Electromagnetic Theory Vector Calculus Fundamental Theorems of Vector Calculus
The value of the line integral for the vector,
\(\vec{v}=2 \hat{x}+y z^2 \hat{y}+\left(3 y+z^2\right) \hat{z} \)
along the closed path OABO (as shown in the figure) is:
(Path AB is the arc of a circle of unit radius)
1
\( \frac{1}{4}(3 \pi-1) \)
2
\( 3 \pi-\frac{1}{4}\)
3
\( \frac{3 \pi}{4}-1 \)
4
3π - 1