ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral from 0 to 1 of x^2e^{-15x}

解

\int_{0}^{1} x^{2} e^{- 15 x} d x

解

\frac{2 e ^{15} - 257}{3375 e ^{15}}

+1

十進法表記

0.00059 \dots

解答ステップ

\int_{0}^{1} x^{2} e^{- 15 x} d x

u置換積分法を適用する

= \int_{0}^{- 15} - \frac{e ^{u} u ^{2}}{3375} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 15}^{0} - \frac{e ^{u} u ^{2}}{3375} d u

定数を除く:

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

= - (- \frac{1}{3375} \cdot \int_{- 15}^{0} e^{u} u^{2} d u)

部分積分を適用する

= - (- \frac{1}{3375} [u^{2} e^{u} - \int 2 u e^{u} d u]_{- 15}^{0})

\int 2 u e^{u} d u = 2 (e^{u} u - e^{u})

= - (- \frac{1}{3375} [u^{2} e^{u} - 2 (e^{u} u - e^{u})]_{- 15}^{0})

簡素化

= \frac{1}{3375} [e^{u} u^{2} - 2 (e^{u} u - e^{u})]_{- 15}^{0}

限度を計算する:

2 - \frac{257}{e ^{15}}

= \frac{1}{3375} (2 - \frac{257}{e ^{15}})

簡素化

= \frac{2 e ^{15} - 257}{3375 e ^{15}}

グラフ

人気の例

integral from 1 to 3 of 10x^4

\int_{1}^{3} 10 x^{4} d x

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

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

integral from 3 to infinity of 1/(ln(x))

\int_{3}^{\infty} \frac{1}{ln ( x )} d x

integral from-1 to 3 of (-x^3-5x+1)

\int_{- 1}^{3} (- x^{3} - 5 x + 1) d x

integral from 1 to 2 of (ln(4x))^2

\int_{1}^{2} (ln (4 x))^{2} d x