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人気のある微分積分 >

integral from 0 to 1 of 1/(2+cos(pix))

解

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

解

\frac{1}{3}

+1

十進法表記

0.57735 \dots

解答ステップ

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

不定積分を計算する:

\int \frac{1}{2 + cos ( π x )} d x = \frac{2}{3 π} arctan (\frac{1}{3} tan (\frac{π x}{2})) + C

限度を計算する:

\int_{0}^{1} \frac{1}{2 + cos ( π x )} d x = \frac{1}{3} - 0

= \frac{1}{3} - 0

簡素化

= \frac{1}{3}

グラフ

人気の例

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\int_{- π}^{0} (t + \frac{π}{2}) cos (n t) d t

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\int_{0}^{2} \frac{3 x}{4} d x

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\int_{- 3}^{5} [2 y - (y^{2} - 15)] d y

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