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人気のある微分積分 >

integral from 0 to t of xsin(t-x)

解

\int_{0}^{t} x sin (t - x) d x

解

t - sin (t)

解答ステップ

\int_{0}^{t} x sin (t - x) d x

部分積分を適用する

= [x cos (t - x) - \int cos (t - x) d x]_{0}^{t}

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

= [x cos (t - x) - (- sin (t - x))]_{0}^{t}

簡素化

= [x cos (t - x) + sin (t - x)]_{0}^{t}

限度を計算する:

t - sin (t)

= t - sin (t)

人気の例

integral from 0 to 2 of 10x^2

\int_{0}^{2} 10 x^{2} d x

integral from 0 to pi of sqrt(x^4+4x^2)

\int_{0}^{π} x^{4} + 4 x^{2} d x

integral from 9 to 15 of (x-8)^{-2/3}

\int_{9}^{15} (x - 8)^{- \frac{2}{3}} d x

integral from 0 to pi of sin^5(θ)

\int_{0}^{π} sin^{5} (θ) d θ

integral from 0 to 7 of x/(x^2+1)

\int_{0}^{7} \frac{x}{x ^{2} + 1} d x