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 pi to 0 of sin^4(x)

解

\int_{π}^{0} sin^{4} (x) d x

解

- \frac{3 π}{8}

+1

十進法表記

- 1.17809 \dots

解答ステップ

\int_{π}^{0} sin^{4} (x) d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{π} sin^{4} (x) d x

積分換算を適用する

= - (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \int_{0}^{π} sin^{2} (x) d x)

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

= - (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2})

簡素化

- (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2}) : [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} - \frac{3 π}{8}

= [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} - \frac{3 π}{8}

限度を計算する:

0

= 0 - \frac{3 π}{8}

簡素化

= - \frac{3 π}{8}

グラフ

人気の例

integral from 1 to 2 of (-4t^{-4})

\int_{1}^{2} (- 4 t^{- 4}) d t

integral from x to x^2 of e^{-t^2}

\int_{x}^{x^{2}} e^{- t^{2}} d t

integral from 1 to 6 of (3(ln(x))^2)/x

\int_{1}^{6} \frac{3 ( ln ( x ) ) ^{2}}{x} d x

integral from 2 to x of t

\int_{2}^{x} t d t

integral from 0 to pi/4 of-cos(x)

\int_{0}^{\frac{π}{4}} - cos (x) d x