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 pi/2 of sin^6(x)

解

\int_{0}^{\frac{π}{2}} sin^{6} (x) d x

解

\frac{5 π}{32}

+1

十進法表記

0.49087 \dots

解答ステップ

\int_{0}^{\frac{π}{2}} sin^{6} (x) d x

積分換算を適用する

= - [\frac{cos ( x ) sin ^{5} ( x )}{6}]_{0}^{\frac{π}{2}} + \frac{5}{6} \cdot \int_{0}^{\frac{π}{2}} sin^{4} (x) d x

\int_{0}^{\frac{π}{2}} sin^{4} (x) d x = \frac{3 π}{16}

= - [\frac{cos ( x ) sin ^{5} ( x )}{6}]_{0}^{\frac{π}{2}} + \frac{5}{6} \cdot \frac{3 π}{16}

簡素化

- [\frac{cos ( x ) sin ^{5} ( x )}{6}]_{0}^{\frac{π}{2}} + \frac{5}{6} \cdot \frac{3 π}{16} : - [\frac{1}{6} sin^{5} (x) cos (x)]_{0}^{\frac{π}{2}} + \frac{5 π}{32}

= - [\frac{1}{6} sin^{5} (x) cos (x)]_{0}^{\frac{π}{2}} + \frac{5 π}{32}

限度を計算する:

0

= - 0 + \frac{5 π}{32}

簡素化

= \frac{5 π}{32}

グラフ

人気の例

integral of (2+sqrt(x))/(2-sqrt(x))

\int \frac{2 + x}{2 - x} d x

integral from-2 to 9 of 7/((4x-3)^2)

\int_{- 2}^{9} \frac{7}{( 4 x - 3 ) ^{2}} d x

integral of 24y(x-yx-(x^2)/2)

\int 24 y (x - y x - \frac{x ^{2}}{2}) d y

integral of x(x+3)

\int x (x + 3) d x

t an g e n t 2 x e^{x}