Question

The value of the line integral for the vector,
$\overrightarrow𝑣=2𝑥̂ +𝑦𝑧 ^2𝑦̂ +(3𝑦+𝑧 ^2 )𝑧̂$
along the closed path OABO (as shown in the figure) is:

(Path AB is the arc of a circle of unit radius)

• A. $\frac{1}{4}(3\pi-1)$
• B. $3\pi-\frac{1}{4}$
• C. $\frac{3\pi}{4}-1$
• D. ${3\pi}-1$

Answer 1

Answer: (A)

$\frac{1}{4}(3\pi-1)$

Answer 2

The correct option is (A): $\frac{1}{4}(3\pi-1)$