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 2 to 4 of sqrt(3+x^2)

解

\int_{2}^{4} 3 + x^{2} d x

解

219 - 7 + \frac{3}{2} ln (\frac{4}{3} + \frac{19}{3}) - \frac{3}{2} ln (\frac{2}{3} + \frac{7}{3})

+1

十進法表記

6.95310 \dots

解答ステップ

\int_{2}^{4} 3 + x^{2} d x

三角関数による置換を適用する

= \int_{a r c t a n (\frac{2}{3})}^{a r c t a n (\frac{4}{3})} 3 sec^{3} (u) d u

定数を除く:

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

= 3 \cdot \int_{a r c t a n (\frac{2}{3})}^{a r c t a n (\frac{4}{3})} sec^{3} (u) d u

積分換算を適用する

= 3 [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{a r c t a n (\frac{2}{3})}^{a r c t a n (\frac{4}{3})} + \frac{1}{2} \cdot \int_{a r c t a n (\frac{2}{3})}^{a r c t a n (\frac{4}{3})} sec (u) d u

\int_{a r c t a n (\frac{2}{3})}^{a r c t a n (\frac{4}{3})} sec (u) d u = ln (\frac{4}{3} + \frac{19}{3}) - ln (\frac{2}{3} + \frac{7}{3})

= 3 [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{a r c t a n (\frac{2}{3})}^{a r c t a n (\frac{4}{3})} + \frac{1}{2} (ln (\frac{4}{3} + \frac{19}{3}) - ln (\frac{2}{3} + \frac{7}{3}))

簡素化

3 [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{a r c t a n (\frac{2}{3})}^{a r c t a n (\frac{4}{3})} + \frac{1}{2} (ln (\frac{4}{3} + \frac{19}{3}) - ln (\frac{2}{3} + \frac{7}{3})) : 3 [\frac{1}{2} sec (u) tan (u)]_{a r c t a n (\frac{2}{3})}^{a r c t a n (\frac{4}{3})} + \frac{3}{2} ln (\frac{4}{3} + \frac{19}{3}) - \frac{3}{2} ln (\frac{2}{3} + \frac{7}{3})

= 3 [\frac{1}{2} sec (u) tan (u)]_{a r c t a n (\frac{2}{3})}^{a r c t a n (\frac{4}{3})} + \frac{3}{2} ln (\frac{4}{3} + \frac{19}{3}) - \frac{3}{2} ln (\frac{2}{3} + \frac{7}{3})

限度を計算する:

\frac{2 19 - 7}{3}

= 3 \cdot \frac{2 19 - 7}{3} + \frac{3}{2} ln (\frac{4}{3} + \frac{19}{3}) - \frac{3}{2} ln (\frac{2}{3} + \frac{7}{3})

簡素化

= 219 - 7 + \frac{3}{2} ln (\frac{4}{3} + \frac{19}{3}) - \frac{3}{2} ln (\frac{2}{3} + \frac{7}{3})

グラフ

人気の例

integral from 2 to 6 of 6x^2ln(3x)

\int_{2}^{6} 6 x^{2} ln (3 x) d x

integral from 0 to k of sin^2(10pit)

\int_{0}^{k} sin^{2} (10 π t) d t

integral from 1 to 3 of (1+2y)

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

integral from 0 to 4 of (36)/(x^2+9)

\int_{0}^{4} \frac{36}{x ^{2} + 9} d x

integral from 0 to pi of 1/(4x^2-4x+5)

\int_{0}^{π} \frac{1}{4 x ^{2} - 4 x + 5} d x