Green's Theorem

Q. The value of ${\int }_c[(3x-8y^2)dx+(4y-6xy\left)dy\right]$, where C is the boundary of the region bounded by x = 0, y = 0 and x + y = 1 is_____

1. 1.67

Q. Value of the integral ${\oint }_c(xydy-y^{2}dx)$, where C is the square cut from the first quadrant by the lines x = 1 and y = 1 will be (use Green's theorem to change the line integral into double integral)

1. $\frac{1}{2}$
2. 1
3. $\frac{3}{2}$
4. $\frac{5}{3}$

Q. Let C be the curve x = 4 - $y^2$ from (0, -2) to (0, 2). Then the value of integral ${\int }_C(y^{3}dx+x^{2}dy)$ will be

1. $\frac{64}{15}$
2. 0
3. $\frac{128}{15}$
4. $\frac{72}{5}$