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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{2 2 - 1}{3}

Decimal

0.60947 \dots

Solution steps

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

Apply u-substitution

= \int_{1}^{2} u^{2} d u

Apply the Power Rule

= [\frac{u ^{3}}{3}]_{1}^{2}

Compute the boundaries:

\frac{2 2}{3} - \frac{1}{3}

= \frac{2 2}{3} - \frac{1}{3}

Simplify

= \frac{2 2 - 1}{3}

\int \frac{1}{7 x ^{7}} d x

\frac{d}{d x} (sin (4 x) + 2 x^{\frac{3}{2}})

sin (x), x = \frac{π}{4}

\frac{d}{d x} ((ln (x)) d x)

x \to - 1 + lim (2 x + 2)

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