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 2 of sqrt(4t^2+5)

解

\int_{- 1}^{2} 4 t^{2} + 5 d t

解

\frac{1}{8} (4 (221 + 3) + 10 ln (\frac{4}{5} + \frac{21}{5}) + 5 ln (5))

+1

十進法表記

8.76974 \dots

解答ステップ

\int_{- 1}^{2} 4 t^{2} + 5 d t

三角関数による置換を適用する

= \int_{- a r c t a n (\frac{2}{5})}^{a r c t a n (\frac{4}{5})} \frac{5}{2} sec^{3} (u) d u

定数を除く:

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

= \frac{5}{2} \cdot \int_{- a r c t a n (\frac{2}{5})}^{a r c t a n (\frac{4}{5})} sec^{3} (u) d u

積分換算を適用する

= \frac{5}{2} [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{- a r c t a n (\frac{2}{5})}^{a r c t a n (\frac{4}{5})} + \frac{1}{2} \cdot \int_{- a r c t a n (\frac{2}{5})}^{a r c t a n (\frac{4}{5})} sec (u) d u

\int_{- a r c t a n (\frac{2}{5})}^{a r c t a n (\frac{4}{5})} sec (u) d u = ln (\frac{4}{5} + \frac{21}{5}) + \frac{1}{2} ln (5)

= \frac{5}{2} [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{- a r c t a n (\frac{2}{5})}^{a r c t a n (\frac{4}{5})} + \frac{1}{2} (ln (\frac{4}{5} + \frac{21}{5}) + \frac{1}{2} ln (5))

簡素化

\frac{5}{2} [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{- a r c t a n (\frac{2}{5})}^{a r c t a n (\frac{4}{5})} + \frac{1}{2} (ln (\frac{4}{5} + \frac{21}{5}) + \frac{1}{2} ln (5)) : \frac{1}{8} 20 [\frac{sec ( u ) tan ( u )}{2}]_{- a r c t a n (\frac{2 5}{5})}^{a r c t a n (\frac{4 5}{5})} + 10 ln (\frac{4}{5} + \frac{21}{5}) + 5 ln (5)

= \frac{1}{8} 20 [\frac{sec ( u ) tan ( u )}{2}]_{- a r c t a n (\frac{2 5}{5})}^{a r c t a n (\frac{4 5}{5})} + 10 ln (\frac{4}{5} + \frac{21}{5}) + 5 ln (5)

限度を計算する:

\frac{2 21}{5} + \frac{3}{5}

= \frac{1}{8} (20 (\frac{2 21}{5} + \frac{3}{5}) + 10 ln (\frac{4}{5} + \frac{21}{5}) + 5 ln (5))

簡素化

= \frac{1}{8} (4 (221 + 3) + 10 ln (\frac{4}{5} + \frac{21}{5}) + 5 ln (5))

グラフ

人気の例

integral from 0 to 2 of 6x(4-x)

\int_{0}^{2} 6 x (4 - x) d x

integral from 0 to pi/(18) of sin^5(9x)

\int_{0}^{\frac{π}{18}} sin^{5} (9 x) d x

integral from 0 to 5 of 2x-5

\int_{0}^{5} 2 x - 5 d x

integral from 0 to ln(2) of e^{2x}-e^x

\int_{0}^{l n (2)} e^{2 x} - e^{x} d x

integral from 1 to sqrt(3 of)arctan(1/r)

\int_{1}^{3} arctan (\frac{1}{r}) d r