What is the integral from 0 to 1 of 3xsqrt(x^2+4) ?

The integral from 0 to 1 of 3xsqrt(x^2+4) is 5sqrt(5)-8

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 3xsqrt(x^2+4)

\int_{0}^{1} 3 x x^{2} + 4 d x

55 - 8

Decimal

3.18033 \dots

Solution steps

\int_{0}^{1} 3 x x^{2} + 4 d x

Take the constant out:

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

= 3 \cdot \int_{0}^{1} x x^{2} + 4 d x

Apply u-substitution

= 3 \cdot \int_{2}^{5} u^{2} d u

Apply the Power Rule

= 3 [\frac{u ^{3}}{3}]_{2}^{5}

Compute the boundaries:

\frac{5 5}{3} - \frac{8}{3}

= 3 (\frac{5 5}{3} - \frac{8}{3})

Simplify

= 55 - 8

What is the integral from 0 to 1 of 3xsqrt(x^2+4) ?
The integral from 0 to 1 of 3xsqrt(x^2+4) is 5sqrt(5)-8