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 2pi of (cos(x))^4

解

\int_{0}^{2 π} (cos (x))^{4} d x

解

\frac{3 π}{4}

+1

十進法表記

2.35619 \dots

解答ステップ

\int_{0}^{2 π} (cos (x))^{4} d x

簡素化

= \int_{0}^{2 π} cos^{4} (x) d x

簡素化

cos^{4} (x) : cos^{3} (x) cos (x)

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

部分積分を適用する

= [cos^{3} (x) sin (x) - \int - 3 cos^{2} (x) sin^{2} (x) d x]_{0}^{2 π}

\int - 3 cos^{2} (x) sin^{2} (x) d x = - \frac{3}{8} (x - \frac{1}{4} sin (4 x))

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

簡素化

[cos^{3} (x) sin (x) - (- \frac{3}{8} (x - \frac{1}{4} sin (4 x)))]_{0}^{2 π} : [\frac{1}{32} (32 cos^{3} (x) sin (x) + 3 (4 x - sin (4 x)))]_{0}^{2 π}

= [\frac{1}{32} (32 cos^{3} (x) sin (x) + 3 (4 x - sin (4 x)))]_{0}^{2 π}

限度を計算する:

\frac{3 π}{4}

= \frac{3 π}{4}

グラフ

人気の例

integral from-2 to 0 of 1/((2-1)^3)

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

integral from-7 to 3 of |x|

\int_{- 7}^{3} ∣ x ∣ d x

integral from 0 to 1 of arcsin(sqrt(x))

\int_{0}^{1} arcsin (x) d x

integral from 0 to 1 of 4pix

\int_{0}^{1} 4 π x d x

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

\int_{0}^{2} 1 + x^{2} d x