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 1/2 to 1/3 of (cos(piw))

解

\int_{\frac{1}{2}}^{\frac{1}{3}} (cos (π w)) d w

解

- \frac{2 - 3}{2 π}

+1

十進法表記

- 0.04264 \dots

解答ステップ

\int_{\frac{1}{2}}^{\frac{1}{3}} cos (π w) d w

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

= - \int_{\frac{1}{3}}^{\frac{1}{2}} cos (π w) d w

u置換積分法を適用する

= - \int_{\frac{π}{3}}^{\frac{π}{2}} cos (u) \frac{1}{π} d u

定数を除く:

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

= - \frac{1}{π} \cdot \int_{\frac{π}{3}}^{\frac{π}{2}} cos (u) d u

共通積分を使用する:

\int cos (u) d u = sin (u)

= - \frac{1}{π} [sin (u)]_{\frac{π}{3}}^{\frac{π}{2}}

限度を計算する:

1 - \frac{3}{2}

= - \frac{1}{π} (1 - \frac{3}{2})

簡素化

= - \frac{2 - 3}{2 π}

グラフ

人気の例

integral from-2 to 3 of 1-x

\int_{- 2}^{3} 1 - x d x

integral from 1 to infinity of tan(x)

\int_{1}^{\infty} tan (x) d x

integral from 1/2 to 2 of 2x-1

\int_{\frac{1}{2}}^{2} 2 x - 1 d x

integral from 0 to 1 of 5x(5x^2+1)

\int_{0}^{1} 5 x (5 x^{2} + 1) d x

integral from 0 to 1 of 2/((x+1)(x+3))

\int_{0}^{1} \frac{2}{( x + 1 ) ( x + 3 )} d x