# the line integral    (1,2,3) (2,0,0) (xdx ydy zdz) is independent of path or not.

Grade:12th pass

## 3 Answers

Arun
25757 Points
3 years ago
Dear student

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avinash kumar
14 Points
3 years ago
1.
1. Describe the Taylor’s theorem for functions of two variables Jacobeans.

2. Evaluate ]dxdy )x y(dzdx )y z(dydz )x z([ S ∫∫ + + + + + where S: x2 +y2 +z2 = 1

3. Find volume of the region bounded by the first octant section cut from the region inside the cylinder x2 +y2 =1 and by the planes y=0, z=0, x=y.

4. In usual notations prove that, = ∫∫∫ R f dv 2 ∫∫ S dA.

5. In usual notations prove that, = ∫∫∫ R f dv 2 ∫∫ S dA

6. Evaluate 1 0 2 2 2 0 x y dxdy π .

7.

8. Check whether the line integral + + (1,2,3) (2,0,0) (xdx ydy zdz) is independent of path or not.

9. Verify Stoke's theorem for v y i x j 3 3  and surface S: the circular disk = x 2 +y2 1, z=0.

Vikas TU
14149 Points
3 years ago
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