On an Exam, Students Were Asked to Evaluate $\int _ { C } \left( x ^ { 2 } \vec { i } + x \vec { j } \right) \cdot d \vec { r }$

question 44

Essay

On an exam, students were asked to evaluate $\int _ { C } \left( x ^ { 2 } \vec { i } + x \vec { j } \right) \cdot d \vec { r }$ , where C has the parameterization $x = \cos t , y = \sin t , 0 \leq t \leq \pi$ .One student wrote:
"Using Green's Theorem, $\int _ { C } \left( x ^ { 2 } \vec { i } + x \vec { j } \right) \cdot d \vec { r } = \int _ { D } \left( \frac { \partial x } { \partial x } - \frac { \partial \left( x ^ { 2 } \right) } { \partial y } \right) d A = \int _ { D } 1 d A =$ Area of the semi-circle = $\frac { \pi } { 2 }$ ."
Do you agree with the student?

Understand the process and significance of cell differentiation during prenatal development.

Identify the challenges and considerations regarding prenatal testing and viability.

Describe the process and outcomes of prenatal implantation and development of the placenta.

Understand the impact of genetic disorders on prenatal and postnatal development.

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