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人気のある微分積分 >

integral from 0 to 4 of pi(x^2)^2

解

\int_{0}^{4} π (x^{2})^{2} d x

解

\frac{1024 π}{5}

+1

十進法表記

643.39817 \dots

解答ステップ

\int_{0}^{4} π (x^{2})^{2} d x

定数を除く:

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

= π \cdot \int_{0}^{4} (x^{2})^{2} d x

簡素化

(x^{2})^{2} : x^{4}

= π \cdot \int_{0}^{4} x^{4} d x

べき乗則を適用する

= π [\frac{x ^{5}}{5}]_{0}^{4}

限度を計算する:

\frac{1024}{5}

= π \frac{1024}{5}

簡素化

= \frac{1024 π}{5}

グラフ

人気の例

integral from 3 to 6 of (9-2x)

\int_{3}^{6} (9 - 2 x) d x

integral from 0 to pi of 1/2 (4sin(x))^2

\int_{0}^{π} \frac{1}{2} (4 sin (x))^{2} d x

integral from 2 to 22 of x^4

\int_{2}^{22} x^{4} d x

integral from-2 to 4 of (x^2)/2

\int_{- 2}^{4} \frac{x ^{2}}{2} d x

integral from 0 to 4 of (3^x)/(e^x)

\int_{0}^{4} \frac{3 ^{x}}{e ^{x}} d x