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/2 to pi/2 of 4cos^6(θ)

解

\int_{- \frac{π}{2}}^{\frac{π}{2}} 4 cos^{6} (θ) d θ

解

\frac{5 π}{4}

+1

十進法表記

3.92699 \dots

解答ステップ

\int_{- \frac{π}{2}}^{\frac{π}{2}} 4 cos^{6} (θ) d θ

定数を除く:

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

= 4 \cdot \int_{- \frac{π}{2}}^{\frac{π}{2}} cos^{6} (θ) d θ

積分換算を適用する

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

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos^{4} (θ) d θ = \frac{3 π}{8}

= 4 ([\frac{sin ( θ ) cos ^{5} ( θ )}{6}]_{- \frac{π}{2}}^{\frac{π}{2}} + \frac{5}{6} \cdot \frac{3 π}{8})

簡素化

4 ([\frac{sin ( θ ) cos ^{5} ( θ )}{6}]_{- \frac{π}{2}}^{\frac{π}{2}} + \frac{5}{6} \cdot \frac{3 π}{8}) : 4 ([\frac{1}{6} cos^{5} (θ) sin (θ)]_{- \frac{π}{2}}^{\frac{π}{2}} + \frac{5 π}{16})

= 4 ([\frac{1}{6} cos^{5} (θ) sin (θ)]_{- \frac{π}{2}}^{\frac{π}{2}} + \frac{5 π}{16})

限度を計算する:

0

= 4 (0 + \frac{5 π}{16})

簡素化

= \frac{5 π}{4}

グラフ

人気の例

integral from-3 to 3 of (4x-2)

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

integral from 2 to 3 of 3x^3-12x

\int_{2}^{3} 3 x^{3} - 12 x d x

integral from pi/2 to 0 of (cos(x))

\int_{\frac{π}{2}}^{0} (cos (x)) d x

integral from-4 to 4 of 9-x^2

\int_{- 4}^{4} 9 - x^{2} d x

integral from 2 to 6 of sqrt(4x-8)

\int_{2}^{6} 4 x - 8 d x