Mohon bantuannya gan.
Matematika
Veendy1
Pertanyaan
Mohon bantuannya gan.
1 Jawaban
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1. Jawaban Anonyme
[tex]\displaystyle 2\pi\int\limits^{\frac12\pi}_0\sin^2\theta\,d\theta=2\pi\int\limits^{\frac12\pi}_0\frac{1-\cos2\theta}{2}\,d\theta\\2\pi\int\limits^{\frac12\pi}_0\sin^2\theta\,d\theta=2\pi\cdot\frac12\int\limits^{\frac12\pi}_01-\cos2\theta\,d\theta\\2\pi\int\limits^{\frac12\pi}_0\sin^2\theta\,d\theta=\pi\left(\left1+\frac12\sin2\theta\right|^{\frac12\pi}_0\right)\\2\pi\int\limits^{\frac12\pi}_0\sin^2\theta\,d\theta=\pi\left(1+\frac12\sin\left(2\cdot\frac12\pi\right)-1-\frac12\sin2\cdot0\right)[/tex]
[tex]\displaystyle 2\pi\int\limits^{\frac12\pi}_0\sin^2\theta\,d\theta=\pi\left(1+\frac12\sin\pi-1-\frac12\sin0\right)\\2\pi\int\limits^{\frac12\pi}_0\sin^2\theta\,d\theta=\pi(1+0-1-0)\\\boxed{\boxed{2\pi\int\limits^{\frac12\pi}_0\sin^2\theta\,d\theta=0}}[/tex]