Calculate the Circulation of the Field F Around the Closed $\mathbf { F } = \frac { 7 } { 10 } \mathrm { x } ^ { 2 } \mathrm { yi } + \frac { 7 } { 10 } \mathrm { xy } ^ { 2 } \mathrm { j } ;$

question 122

Multiple Choice

Calculate the circulation of the field F around the closed curve C.
- $\mathbf { F } = \frac { 7 } { 10 } \mathrm { x } ^ { 2 } \mathrm { yi } + \frac { 7 } { 10 } \mathrm { xy } ^ { 2 } \mathrm { j } ;$ curve $\mathrm { C }$ is $\mathbf { r } ( \mathrm { t } ) = 3 \cos \mathrm { ti } + 3 \sin \mathrm { tj } , 0 \leq \mathrm { t } \leq 2 \pi$

• A) \(\frac { 21 } { 10 }\)
• B) \(\frac { 21 } { 5 }\)
• C) \(\frac { 7 } { 5 }\)
• D) 0

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Definitions:

Type II Error

The error that occurs when a false null hypothesis is not rejected.

Type I Error

The incorrect rejection of a true null hypothesis, also known as a "false positive," occurring when a statistical test falsely indicates the presence of an effect.

Type I Error

A statistical error made by rejecting the null hypothesis when it is actually true, known as a false positive.