integral

por giovannixaviermisselli Sáb 31 Ago 2019, 18:27

Ache a integral de $integral 07ba0e8ff5b4ad7ae76a0794d50309d6e276919c$ x^2 sqrt (16 - x^2) dx

por SnoopLy Sáb 31 Ago 2019, 19:15

32 \int 1-\cos \theta \ \mathrm{d\theta}\int x^2 \sqrt{16-x^2}dx

x=16\sin \theta

\mathrm{dx}=16\cos\theta \mathrm{d\theta}}

\int (16\sin \theta)^24\cos \theta \mathrm{dx}=\int (16\cdot 16 \sin^2 \theta )4\cos \theta \mathrm{dx}

\int 64 \sin^2 \theta \mathrm{d\theta}

32 \int 1-\cos \theta \mathrm{d\theta}

32 \left(\int 1 \mathrm{d\theta} - \int \cos \theta \mathrm{d\theta}\right)=32(\theta - \sin \theta)=32\left(\arcsin\left(-\frac{x}{16}\right) + \frac{x}{16}\right)

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