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 2 of sqrt(1+t^2)

解

\int_{0}^{2} 1 + t^{2} d t

解

5 + \frac{1}{2} ln (2 + 5)

+1

十進法表記

2.95788 \dots

解答ステップ

\int_{0}^{2} 1 + t^{2} d t

三角関数による置換を適用する

= \int_{0}^{a r c t a n (2)} sec^{3} (u) d u

積分換算を適用する

= [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (2)} + \frac{1}{2} \cdot \int_{0}^{a r c t a n (2)} sec (u) d u

\int_{0}^{a r c t a n (2)} sec (u) d u = ln (2 + 5)

= [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (2)} + \frac{1}{2} ln (2 + 5)

簡素化

[\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (2)} + \frac{1}{2} ln (2 + 5) : [\frac{1}{2} sec (u) tan (u)]_{0}^{a r c t a n (2)} + \frac{1}{2} ln (2 + 5)

= [\frac{1}{2} sec (u) tan (u)]_{0}^{a r c t a n (2)} + \frac{1}{2} ln (2 + 5)

限度を計算する:

5

= 5 + \frac{1}{2} ln (2 + 5)

グラフ

人気の例

integral from 1 to 6 of |2x-6|

\int_{1}^{6} ∣ 2 x - 6 ∣ d x

integral from-3 to x of f(t)

\int_{- 3}^{x} f (t) d t

integral from 0 to 2pi of 1+cos^2(x)

\int_{0}^{2 π} 1 + cos^{2} (x) d x

integral from 4 to 36 of 4/(sqrt(x))

\int_{4}^{36} \frac{4}{x} d x

integral from 0 to 2 of 3x^2-4x+2

\int_{0}^{2} 3 x^{2} - 4 x + 2 d x