If \(\vec{A} =(3x^2+6y)\hat{i}—14yz\hat{j} +20xz^2\hat{k}\), then the line integral \(\int\limits_{C} \vec{A}.d\bar{r}\) from (0.0, 0) to (1, 1.1), along the curve C ;x=t, y=t². z=t³ is:

Updated On: Sep 25, 2024

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The Correct Option is C

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The correct option is(C):5.

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Match List I with List II
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List I		List II
A.	Φ=y²,∇Φ at (1, 1, 1)	I.	\(\hat{i}\)
B.	Φ=x,∇Φ at (1, -1, 2)	II.	\(-6\hat{k}\)
C.	Φ=2x³,∇Φ at (0, 1, 2)	III.	\(2\hat{j}\)
D.	Φ=3z²,∇Φ at (1, 2, -1)	IV.	\(\vec{0}\)

If \(\vec{A} =(3x^2+6y)\hat{i}—14yz\hat{j} +20xz^2\hat{k}\), then the line integral \(\int\limits_{C} \vec{A}.d\bar{r}\) from (0.0, 0) to (1, 1.1), along the curve C ;x=t, y=t2. z=t3 is: