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 (3pi)/2 of cos^3(29x)

解

\int_{0}^{\frac{3 π}{2}} cos^{3} (29 x) d x

解

- \frac{2}{87}

+1

十進法表記

- 0.02298 \dots

解答ステップ

\int_{0}^{\frac{3 π}{2}} cos^{3} (29 x) d x

u置換積分法を適用する

= \int_{0}^{\frac{87 π}{2}} cos^{3} (u) \frac{1}{29} d u

定数を除く:

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

= \frac{1}{29} \cdot \int_{0}^{\frac{87 π}{2}} cos^{3} (u) d u

三角関数の公式を使用して書き換える

= \frac{1}{29} \cdot \int_{0}^{\frac{87 π}{2}} (1 - sin^{2} (u)) cos (u) d u

u置換積分法を適用する

= \frac{1}{29} \cdot \int_{0}^{- 1} 1 - v^{2} d v

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

= \frac{1}{29} (- \int_{- 1}^{0} 1 - v^{2} d v)

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{29} (- (\int_{- 1}^{0} 1 d v - \int_{- 1}^{0} v^{2} d v))

\int_{- 1}^{0} 1 d v = 1

\int_{- 1}^{0} v^{2} d v = \frac{1}{3}

= \frac{1}{29} (- (1 - \frac{1}{3}))

簡素化

\frac{1}{29} (- (1 - \frac{1}{3})) : - \frac{2}{87}

= - \frac{2}{87}

グラフ

人気の例

derivative of (x^3+3x/(x^2-4x+3))

\frac{d}{d x} (\frac{x ^{3} + 3 x}{x ^{2} - 4 x + 3})

limit as x approaches infinity of-2e^x

x \to \infty lim (- 2 e^{x})

derivative of (2-xe^x)

\frac{d}{d x} ((2 - x) e^{x})

limit as x approaches 4+of (15)/(x-4)

x \to 4 + lim (\frac{15}{x - 4})

integral of sec^2(x/pi)

\int sec^{2} (\frac{x}{π}) d x