Are the following statements true or false? If F = nabla f then F is conservativ

Question

Are the following statements true or false? If F = nabla f then F is conservative. If the vector fields F and G have integral_C F middot dr = integral_C G middot dr for a particular path C, then F = G. If F is conservative, then there is a potential function f such that F = nabla f. The line integral of any vector field F around any closed curve C is zero. For any vector field F, there is always a function f such that integral_C F middot dr = f(Q) - f(P) whenever P and Q are the endpoints of the curve C. If integral_C F middot dr = 0 for one particular closed path, then F is conservative. If integral_C F middot dr notequalto 0 for some closed path C, then F is not conservative. If F is conservative and C is any closed curve, then integral_C F middot dr = 0.

Explanation / Answer

1. True
2.False ( for example : for two different constant function line integral along closed path is zero but they are not equal)
3.True
4.True
5.True
6.False (If for one particular closed path line integral of a constant funstant function or any non constant non conservative function can be zero )
7. True
8.True

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.