Question

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Answer 1

AnsWer :

0.

QuestioN :

$\tt \dagger\: \: \: \: \: \int\limits^{2\pi}_{0} Sin\, \theta \, d\theta$

SolutioN :

$\tt \longmapsto\int\limits^{2\pi}_{0} Sin\, \theta \, d\theta$

✎ Let's Integrate W.r.t.θ

$\tt \longmapsto\Big[-Cos\,\theta\Big]^{2\pi}_{0}$

» Now,

• Putting the given limits.

$\tt \longmapsto\Big[-Cos\,2 \pi \Big] -\Big[ -Cos\,0 \Big]$

✰Now, We need to Know,

• The value of Cos 2π and Cos 0°
• Cos 2π = Cos 2 * 180° → Cos 360° → 1.
• Cos 0° = 1.

$\tt \longmapsto\Big[-1 \Big] -\Big[ -1 \Big]$

$\tt \longmapsto\Big[-1 + 1 \Big]$

$\tt \longmapsto0.$

♢ Therefore, the value of given integration is 0.