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人気のある微分積分 >

integral from 0 to cos(x) of ysin(x)

解

\int_{0}^{c o s (x)} y sin (x) d y

解

\frac{cos ^{2} ( x ) sin ( x )}{2}

解答ステップ

\int_{0}^{c o s (x)} y sin (x) d y

定数を除く:

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

= sin (x) \cdot \int_{0}^{c o s (x)} y d y

べき乗則を適用する

= sin (x) [\frac{y ^{2}}{2}]_{0}^{c o s (x)}

限度を計算する:

\frac{cos ^{2} ( x )}{2}

= sin (x) \frac{cos ^{2} ( x )}{2}

簡素化

= \frac{cos ^{2} ( x ) sin ( x )}{2}

人気の例

integral from 0 to 7 of (2xsqrt(x^2-1))

\int_{0}^{7} (2 x x^{2} - 1) d x

integral from pi/3 to pi/6 of tan^2(x)

\int_{\frac{π}{3}}^{\frac{π}{6}} tan^{2} (x) d x

integral from-1 to 3 of e^x-3

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

integral from 0 to 1 of (1-e^2)^{1/2}

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

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

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