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人気のある微分積分 >

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

解

\int_{0}^{\frac{x}{2}} f (cos (x)) d x

解

f sin (\frac{x}{2})

解答ステップ

\int_{0}^{\frac{x}{2}} f cos (x) d x

定数を除く:

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

= f \cdot \int_{0}^{\frac{x}{2}} cos (x) d x

共通積分を使用する:

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

= f [sin (x)]_{0}^{\frac{x}{2}}

限度を計算する:

sin (\frac{x}{2})

= f sin (\frac{x}{2})

人気の例

integral from 1 to e of (1+x+x^3)/x

\int_{1}^{e} \frac{1 + x + x ^{3}}{x} d x

integral from 1 to 3 of (5/x-e^{-x})

\int_{1}^{3} (\frac{5}{x} - e^{- x}) d x

integral from-2 to 1 of (2x^2-1)^2

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

integral from 1 to 2 of e^{sqrt(x-1)}

\int_{1}^{2} e^{x - 1} d x

integral from 0 to 8 of-6x^2-6x+432

\int_{0}^{8} - 6 x^{2} - 6 x + 432 d x