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人気のある微分積分 >

integral from 0 to (2pi)/4 of integral from 1 to 2 of sqrt(4-r^2)*r

解

\int_{0}^{\frac{2 π}{4}} \int_{1}^{2} 4 - r^{2} \cdot r d r d θ

解

\frac{3 π}{2}

+1

十進法表記

2.72069 \dots

解答ステップ

\int_{0}^{\frac{2 π}{4}} \int_{1}^{2} 4 - r^{2} r d r d θ

\int_{1}^{2} 4 - r^{2} r d r = 3

= \int_{0}^{\frac{2 π}{4}} 3 d θ

\int_{0}^{\frac{2 π}{4}} 3 d θ = \frac{3 π}{2}

= \frac{3 π}{2}

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