Question

2. State the prove Stoke's theorem.
स्टोक्स प्रमेय लिखो और सिद्ध करो।​

Answer 1

Step-by-step explanation:

The Stoke's theorem states that “the surface integral of the curl of a function over a surface bounded by a closed surface is equal to the line integral of the particular vector function around that surface.” Where, C = A closed curve. S = Any surface bounded by C.

Answer 2

• We will prove Stokes' theorem for a vector field of the form P (x, y, z) k .

• That is, we will show, with the usual notations, (3) P (x, y, z) dz = curl (P k ) · n dS .

• (3) P (x, y, z) dz = curl (P k ) ·

• We assume S is given as the graph of z = f(x, y) over a region R of the xy-plane

• We let C be the boundary of S, and C the boundary of R.