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人気のある微分積分 >

integral from 0 to pi of sin(n)x

解

\int_{0}^{π} sin (n) x d x

解

sin (n) \frac{π ^{2}}{2}

解答ステップ

\int_{0}^{π} sin (n) x d x

定数を除く:

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

= sin (n) \cdot \int_{0}^{π} x d x

べき乗則を適用する

= sin (n) [\frac{x ^{2}}{2}]_{0}^{π}

限度を計算する:

\frac{π ^{2}}{2}

= sin (n) \frac{π ^{2}}{2}

人気の例

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

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

integral from 0 to 2 of (8-2x)

\int_{0}^{2} (8 - 2 x) d x

integral from-2 to 2 of (6-x^2)-|x|

\int_{- 2}^{2} (6 - x^{2}) - ∣ x ∣ d x

integral from-pi to pi of |sin(t)|

\int_{- π}^{π} ∣ sin (t) ∣ d t

integral from 0 to 1 of x^{1/2}-x^2

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