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人気のある微分積分 >

integral from-1 to 1 of (-30x^2+4xy)

解

\int_{- 1}^{1} (- 30 x^{2} + 4 x y) d y

解

- 60 x^{2}

解答ステップ

\int_{- 1}^{1} - 30 x^{2} + 4 x y d y

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{- 1}^{1} 30 x^{2} d y + \int_{- 1}^{1} 4 x y d y

\int_{- 1}^{1} 30 x^{2} d y = 60 x^{2}

\int_{- 1}^{1} 4 x y d y = 0

= - 60 x^{2} + 0

簡素化

= - 60 x^{2}

人気の例

integral from 0 to 5 of |t^2+2t-15|

\int_{0}^{5} t^{2} + 2 t - 15 d t

integral from 0 to 2 of 1/((2-x)^{5/2)}

\int_{0}^{2} \frac{1}{( 2 - x ) ^{\frac{5}{2}}} d x

integral from 2 to 4 of (2x)

\int_{2}^{4} (2 x) d x

integral from-2 to 1 of (2x^3+4x^2-x+3)

\int_{- 2}^{1} (2 x^{3} + 4 x^{2} - x + 3) d x

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

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