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人気のある微分積分 >

integral from 0 to pi of 1/2 (2θ)^2

解

\int_{0}^{π} \frac{1}{2} (2 θ)^{2} d θ

解

\frac{2 π ^{3}}{3}

+1

十進法表記

20.67085 \dots

解答ステップ

\int_{0}^{π} \frac{1}{2} (2 θ)^{2} d θ

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{π} (2 θ)^{2} d θ

簡素化

(2 θ)^{2} : 4 θ^{2}

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

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

べき乗則を適用する

= \frac{1}{2} \cdot 4 [\frac{θ ^{3}}{3}]_{0}^{π}

簡素化

\frac{1}{2} \cdot 4 [\frac{θ ^{3}}{3}]_{0}^{π} : 2 [\frac{θ ^{3}}{3}]_{0}^{π}

= 2 [\frac{θ ^{3}}{3}]_{0}^{π}

限度を計算する:

\frac{π ^{3}}{3}

= 2 \cdot \frac{π ^{3}}{3}

簡素化

= \frac{2 π ^{3}}{3}

グラフ

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