State the Fundamental Theorem of Calculus for Line Integrals $\int _ { C } \operatorname { grad } f \cdot d \vec { r } = f ( Q ) - f ( P )$

question 77

Multiple Choice

State the Fundamental Theorem of Calculus for Line Integrals.

• A)Suppose C is a piece-wise smooth oriented path with starting point P and end point Q.Then \(\int _ { C } \operatorname { grad } f \cdot d \vec { r } = f ( Q ) - f ( P )\)
• B)Suppose C is a oriented path with starting point P and end point Q.Then \(\int _ { C } \operatorname { grad } f \cdot d \vec { r } = f ( Q ) - f ( P )\)
• C)Suppose C is a piece-wise smooth oriented path with starting point P and end point Q.If f is a function whose gradient is continuous on the path C, then \(\int _ { C } \operatorname { grad } f \cdot d \vec { r } = f ( Q ) - f ( P )\)
• D)Suppose C is a piece-wise smooth oriented path with starting point P and end point Q.If f is a function whose gradient is continuous on the path C, then \(\int _ { C } \operatorname { grad } f \cdot d \vec { r } = f ( P ) - f ( Q ) .\)

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