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 7 of sqrt(1+x^2)

解

\int_{0}^{7} 1 + x^{2} d x

解

\frac{35}{2} + \frac{1}{2} ln (7 + 52)

+1

十進法表記

26.07079 \dots

解答ステップ

\int_{0}^{7} 1 + x^{2} d x

三角関数による置換を適用する

= \int_{0}^{a r c t a n (7)} 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 (7)} + \frac{1}{2} \cdot \int_{0}^{a r c t a n (7)} sec (u) d u

\int_{0}^{a r c t a n (7)} sec (u) d u = ln (7 + 52)

= [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (7)} + \frac{1}{2} ln (7 + 52)

簡素化

[\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (7)} + \frac{1}{2} ln (7 + 52) : [\frac{1}{2} sec (u) tan (u)]_{0}^{a r c t a n (7)} + \frac{1}{2} ln (7 + 52)

= [\frac{1}{2} sec (u) tan (u)]_{0}^{a r c t a n (7)} + \frac{1}{2} ln (7 + 52)

限度を計算する:

\frac{35}{2}

= \frac{35}{2} + \frac{1}{2} ln (7 + 52)

グラフ

人気の例

(\partial)/(\partial z)(cos(z))

\frac{\partial}{\partial z} (cos (z))

derivative of (dy/(dx))+y=cos(x)

\frac{d}{d x} (\frac{d y}{d x}) + y = cos (x)

integral of sec(x/3)-csc(5x)

\int sec (\frac{x}{3}) - csc (5 x) d x

derivative of sec^5(x^7+4x^6)

\frac{d}{d x} (sec^{5} (x^{7} + 4 x)^{6})

derivative x^{2020}+1/3 x^3-4x^2

d er i v a t i v e x^{2020} + \frac{1}{3} x^{3} - 4 x^{2}