8. Evaluate ∫c(1 + xy²)ds, where C is the upper half of the unit circle x² + y² = 1.

III. Essay Questions: Read the news from Washington, D.C., in the U.S. (50%) The Supreme Court recently heard a significant case regarding student speech, involving 14-year- old Brandi Levy, whose profanity-laced Snapchat post led to her suspension from the cheerleading team at her Pennsylvania high school. The case raises the question of whether public schools can discipline students for off-campus speech. The landmark Tinker v. Des Moines ruling in 1969 established that students do not lose their constitutional rights to freedom of speech at school. However, the contours of this decision have been the subject of ongoing debate. Levy's case differs from Tinker in that it lacks the lofty motives of a protest against war. Rather, it represents teenage frustration. Levy expressed her anger at being kept on the junior varsity cheerleading squad for another year by posting profane words and gestures on Snapchat. Her coaches saw the post and suspended her from the team for a year. Levy's parents filed a federal lawsuit, arguing that her suspension violated her constitutional speech rights. Lower courts agreed with Levy and restored her to the cheerleading team, stating that Tinker does not apply to off-campus speech. The 3rd U.S. Circuit Court of Appeals clarified that it was yet to address the First Amendment implications of off-campus speech involving threats of violence or harassment. However, the school district, education groups, the Biden administration, and anti-bullying organizations argued that the appeals court's decision went too far. They emphasized that public schools should be able to discipline students for off-campus speech, depending on the circumstances. While the school district claimed that its approach allows for addressing disruptive speech and protecting students' rights, critics argue that such an approach would grant schools excessive power to monitor and regulate students' speech beyond school grounds. The American Civil Liberties Union (ACLU), representing Levy, contended that this would stifle students' ability to express frustration and could lead to the regulation of political and religious speech. Levy's case has garnered support from an unlikely alliance of conservative and liberal interest groups, who highlight the dangers of expanding school regulation of off-campus speech. The Alliance Defending Freedom and Christian Legal Society caution against the regulation of religious speech, which they believe provokes debate and inflames passions. Even Mary Beth and John Tinker, central figures in the 1969 case, expressed support for Levy, suggesting that their protest would have included a digital social media component. Though Levy's speech may not be considered politically or religiously important, her case has the potential to shape the legal understanding of student speech rights. She aims to highlight that students should not face punishment for expressing their feelings and thoughts. The Supreme Court's ruling in this case will likely have far-reaching implications for student speech and the regulation of online behavior in the internet age. Adapted from https:/newsela.com/read/student-free-speech-supreme-court/id/2001020589/

8. Evaluate ∫c(1 + xy²)ds, where C is the upper half of the unit circle x² + y² = 1.

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