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人気のある微分積分 >

integral from 0 to pi of cos(kx)

解

\int_{0}^{π} cos (k x) d x

解

0

解答ステップ

\int_{0}^{π} cos (k x) d x

u置換積分法を適用する

= \int_{0}^{kπ} \frac{cos ( u )}{k} d u

定数を除く:

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

= \frac{1}{k} \cdot \int_{0}^{kπ} cos (u) d u

共通積分を使用する:

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

= \frac{1}{k} [sin (u)]_{0}^{kπ}

限度を計算する:

0

= \frac{1}{k} \cdot 0

簡素化

= 0

人気の例

integral from 0 to 18 of pi(sqrt(x))^2

\int_{0}^{18} π (x)^{2} d x

integral from 0 to pi/4 of xsin(5x)

\int_{0}^{\frac{π}{4}} x sin (5 x) d x

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

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

integral from 1 to x of 3x^{-4}

\int_{1}^{x} 3 x^{- 4} d x

integral from 1 to 2 of tsqrt(1/2 t^2+8)

\int_{1}^{2} t \frac{1}{2} t^{2} + 8 d t