ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

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

解

\int_{0}^{4} π (2 x^{2})^{2} d x

解

\frac{4096 π}{5}

+1

十進法表記

2573.59270 \dots

解答ステップ

\int_{0}^{4} π (2 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} (2 x^{2})^{2} d x

簡素化

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

= π \cdot \int_{0}^{4} 4 x^{4} d x

定数を除く:

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

= π 4 \cdot \int_{0}^{4} x^{4} d x

べき乗則を適用する

= π 4 [\frac{x ^{5}}{5}]_{0}^{4}

限度を計算する:

\frac{1024}{5}

= π 4 \cdot \frac{1024}{5}

簡素化

= \frac{4096 π}{5}

グラフ

人気の例

integral from-pi/4 to pi/4 of sec(x)

\int_{- \frac{π}{4}}^{\frac{π}{4}} sec (x) d x

integral from 0 to x of ysqrt(x^2-y^2)

\int_{0}^{x} y x^{2} - y^{2} d y

integral from 0 to 1 of x^3-4x^2+3x

\int_{0}^{1} x^{3} - 4 x^{2} + 3 x d x

integral from 0 to sqrt(1-y^2 of)(x+y)

\int_{0}^{1 - y^{2}} (x + y) d x

integral from 1 to 2 of (e^x)/(1+2e^x)

\int_{1}^{2} \frac{e ^{x}}{1 + 2 e ^{x}} d x