MTH301 Quiz 4 by Attiq Kundi

MTH-301 · Quiz file 4 · KNOWLEDGE FOR US · BY ATTIQ KUNDI

1. If a scalar field V (r) exists for all points on the curve, the _____ with 𝑑𝑟→0,

𝑐

Answer: n

p p V r dr

2. One of the line integral properties is

c Fds

Answer: (

c Pdx Qdy

3. Wallis sine formula when n is even∫ sin xdx 𝜋

Answer: 3 𝜋

4. Integration along two separate paths joining the same two wends points ___

give(s) identical results.

Answer: Does not necessary

5. The grad operator ∇ acts on a (an) ___ and gives a vector.

Answer: Scalar

6. The div operator ∇ acts on a (an) ___ and gives a scalar.

Answer: vector

Answer: 𝝏𝑷 𝝏𝒚 = 𝝏𝑸 𝝏𝒙

8. Wallis sine formula when n is odd

𝜋

Answer: 3 1 𝜋

9. If a vector field exists for all points of the curve C, then for each element of arc we

can form the ____.

Answer: scalar product

10. For line integral with respect to arc length, when x and y are expressed in

parametric form, t

c t I f x y ds f x y Where ds=

Answer: dx dy dt dt dt

11. To evaluate a line integral, the integrand is expressed in term of x, y, z with

Answer: dr dxi dyj dzk

12. The path traversal in calculating the Green’s theorem is ____.

Answer: anticlockwise

13. If the path of integration c joining A and B is divided into two parts AK and KB,

then,

Answer: c AK KB I I I

14. For a path of integration parallel to the x-axis, i.e. x=k, dx=0

Answer: c c I Qdy

15. For a path of integration parallel to the x-axis, i.e. y=k, dy =0

Answer: c c I Pdx

16. In all cases, the actual path of integration involved must be ___ and single-valued.