What is the integral from 0 to 1 of 2+sqrt(2+x^2) ?

The integral from 0 to 1 of 2+sqrt(2+x^2) is 2+(sqrt(3))/2+ln(1/(sqrt(2))+sqrt(3/2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

2 + \frac{3}{2} + ln (\frac{1}{2} + \frac{3}{2})

Decimal

3.52450 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{0}^{1} 2 d x = 2

\int_{0}^{1} 2 + x^{2} d x = \frac{3}{2} + ln (\frac{1}{2} + \frac{3}{2})

= 2 + \frac{3}{2} + ln (\frac{1}{2} + \frac{3}{2})

\int - 40

\frac{d}{d x} (\frac{sin ( 4 x )}{2 + cos ( 4 x )})

\int 4 e^{5 x + e^{5 x}} d x

\frac{d y}{d x} = \frac{x ^{2} - y ^{2}}{3 x y}

\frac{d}{d x} (lo g_{2} (3 x^{2}))

What is the integral from 0 to 1 of 2+sqrt(2+x^2) ?
The integral from 0 to 1 of 2+sqrt(2+x^2) is 2+(sqrt(3))/2+ln(1/(sqrt(2))+sqrt(3/2))