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 1 to 3 of sqrt(1+(2x\sqrt{x^2-1))^2}

解

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

解

\frac{52 + 12 2}{3} - 42 - 2

+1

十進法表記

15.33333 \dots

解答ステップ

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

因数

1 + (2 x x^{2} - 1)^{2} : (2 x + 1)^{2} (2 x - 1)^{2}

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

u置換積分法を適用する

= \int_{2 + 1}^{2 \cdot 3 + 1} \frac{u ( u - 1 )}{2} - \frac{u}{2} d u

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_{2 + 1}^{2 \cdot 3 + 1} \frac{u ( u - 1 )}{2} d u - \int_{2 + 1}^{2 \cdot 3 + 1} \frac{u}{2} d u

\int_{2 + 1}^{2 \cdot 3 + 1} \frac{u ( u - 1 )}{2} d u = \frac{52 + 12 2}{3}

\int_{2 + 1}^{2 \cdot 3 + 1} \frac{u}{2} d u = 42 + 2

= \frac{52 + 12 2}{3} - (42 + 2)

簡素化

= \frac{52 + 12 2}{3} - 42 - 2

グラフ

人気の例

integral from 0 to l of wcos(pi/(2l)x)

\int_{0}^{l} w cos (\frac{π}{2 l} x) d x

integral from 1 to 2 of xlog_{5}(x)

\int_{1}^{2} x lo g_{5} (x) d x

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

\int_{- 1}^{0} \frac{1}{e ^{x} + 1} d x

integral from-1 to 1 of (x^5-x^7)

\int_{- 1}^{1} (x^{5} - x^{7}) d x

integral from 0 to 3 of 4t

\int_{0}^{3} 4 t d t