A scalar potential $\Psi$ has the gradient defined as $\nabla\Psi=yz\hat{i}+xz\hat{j}+xy\hat{k}$ . The value of the integral $\int_c\nabla\Psi.d\overrightarrow{r}$ on the curve $\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$ , where curve C: x=t, y = t 2 , z = 3t 2 (1 ≤ t ≤ 3) is:

Question

A scalar potential $\Psi$  has the gradient defined as   $\nabla\Psi=yz\hat{i}+xz\hat{j}+xy\hat{k}$ . The value of the integral  $\int_c\nabla\Psi.d\overrightarrow{r}$  on the curve  $\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$ , where curve C: x=t, y = t 2 , z = 3t 2 (1 ≤ t ≤ 3) is:

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The correct answer is(D): 726

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Answer

A scalar potential \(\Psi\) has the gradient defined as \(\nabla\Psi=yz\hat{i}+xz\hat{j}+xy\hat{k}\). The value of the integral \(\int_c\nabla\Psi.d\overrightarrow{r}\) on the curve \(\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}\), where curve C: x=t, y = t², z = 3t² (1 ≤ t ≤ 3) is:

The Correct Option is D

Solution and Explanation

Top Questions on Integration

Questions Asked in CUET PG exam

A scalar potential \(\Psi\) has the gradient defined as \(\nabla\Psi=yz\hat{i}+xz\hat{j}+xy\hat{k}\). The value of the integral \(\int_c\nabla\Psi.d\overrightarrow{r}\) on the curve \(\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}\), where curve C: x=t, y = t2, z = 3t2 (1 ≤ t ≤ 3) is:

The Correct Option is D

Solution and Explanation

Top Questions on Integration

Questions Asked in CUET PG exam

A scalar potential \(\Psi\) has the gradient defined as \(\nabla\Psi=yz\hat{i}+xz\hat{j}+xy\hat{k}\). The value of the integral \(\int_c\nabla\Psi.d\overrightarrow{r}\) on the curve \(\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}\), where curve C: x=t, y = t², z = 3t² (1 ≤ t ≤ 3) is: