Teaching MPPSC Assistant Professor Mock Test Series 2025 Engineering Mathematics Calculus Vector Calculus
If P(x, y) and Q(x, y) are scalar functions defined over a domain D with piecewise smooth closed boundary C, then
1
∫ ∫ [∂Q/∂x + ∂P/∂y]dx dy = ∫ P(x, y) dx + Q(x, y) dy
2
∫ ∫ [∂Q/∂x - ∂P/∂y]dx dy = ∫ P(x, y) dx + Q(x, y) dy
3
∫ ∫ [∂Q/∂x - ∂P/∂y]dx dy = ∫ P(x, y) dx - Q(x, y) dy
4
∫ ∫ [∂Q/∂x + ∂P/∂y]dx dy = ∫ P(x, y) dx - Q(x, y) dy