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人気のある微分積分 >

integral from 1 to R of x^{-7/5}

解

\int_{1}^{R} x^{- \frac{7}{5}} d x

解

- \frac{5}{2 R ^{\frac{2}{5}}} + \frac{5}{2}

解答ステップ

\int_{1}^{R} x^{- \frac{7}{5}} d x

べき乗則を適用する

= [- \frac{5}{2 x ^{\frac{2}{5}}}]_{1}^{R}

限度を計算する:

- \frac{5}{2 R ^{\frac{2}{5}}} + \frac{5}{2}

= - \frac{5}{2 R ^{\frac{2}{5}}} + \frac{5}{2}

人気の例

derivative of (6x^5-4x^4+7x(x^3-x^2-1))

\frac{d}{d x} ((6 x^{5} - 4 x^{4} + 7 x) (x^{3} - x^{2} - 1))

(\partial)/(\partial x)(e^{x+y+5})

\frac{\partial}{\partial x} (e^{x + y + 5})

(\partial)/(\partial z)((x-y)/(x+z))

\frac{\partial}{\partial z} (\frac{x - y}{x + z})

y^{''}-2y^'+y=(e^t)/(1+t^2)

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{1 + t ^{2}}

integral from 0 to pi of sin^4(3x)

\int_{0}^{π} sin^{4} (3 x) d x