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人気のある微分積分 >

integral from 0 to sin(x) of e^ycos(x)

解

\int_{0}^{s i n (x)} e^{y} cos (x) d y

解

cos (x) (e^{s i n (x)} - 1)

解答ステップ

\int_{0}^{s i n (x)} e^{y} cos (x) d y

定数を除く:

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

= cos (x) \cdot \int_{0}^{s i n (x)} e^{y} d y

共通積分を使用する:

\int e^{y} d y = e^{y}

= cos (x) [e^{y}]_{0}^{s i n (x)}

限度を計算する:

e^{s i n (x)} - 1

= cos (x) (e^{s i n (x)} - 1)

人気の例

integral from 0 to 1/12 of xln(12x)

\int_{0}^{\frac{1}{12}} x ln (12 x) d x

integral from 0 to pi/4 of ln(cos(x))

\int_{0}^{\frac{π}{4}} ln (cos (x)) d x

integral from-2 to 0 of (x-3)(x+5)

\int_{- 2}^{0} (x - 3) (x + 5) d x

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

\int_{0}^{k} x \cdot x^{2} + 4 d x

integral from 1 to 2 of sqrt(2/x)

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