What is the integral from 0 to 2 of-7x^3sqrt(x^2+4) ?

The integral from 0 to 2 of-7x^3sqrt(x^2+4) is -7*(64sqrt(2)+64)/(15)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of-7x^3sqrt(x^2+4)

\int_{0}^{2} - 7 x^{3} x^{2} + 4 d x

- 7 \cdot \frac{64 2 + 64}{15}

Decimal Notation

- 72.10451 \dots

Solution steps

\int_{0}^{2} - 7 x^{3} x^{2} + 4 d x

Take the constant out:

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

= - 7 \cdot \int_{0}^{2} x^{3} x^{2} + 4 d x

Apply u-substitution

: \int_{2}^{22} (u^{2} - 4) u^{2} d u

= - 7 \cdot \int_{2}^{22} (u^{2} - 4) u^{2} d u

Expand

(u^{2} - 4) u^{2} : u^{4} - 4 u^{2}

= - 7 \cdot \int_{2}^{22} u^{4} - 4 u^{2} d u

Apply the Sum Rule:

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

= - 7 (\int_{2}^{22} u^{4} d u - \int_{2}^{22} 4 u^{2} d u)

\int_{2}^{22} u^{4} d u = \frac{128 2 - 32}{5}

\int_{2}^{22} 4 u^{2} d u = \frac{4 ( 16 2 - 8 )}{3}

= - 7 (\frac{128 2 - 32}{5} - \frac{4 ( 16 2 - 8 )}{3})

Join

\frac{128 2 - 32}{5} - \frac{4 ( 16 2 - 8 )}{3} : \frac{64 2 + 64}{15}

= - 7 \cdot \frac{64 2 + 64}{15}

\frac{d}{d x} ((1 + 4 x)^{\frac{3}{2}})

\int_{0}^{\infty} 2 e^{- 2 x} d x

\frac{d y}{d x}, y = 7 x^{8}

\int 3 x - 4 x d x

What is the integral from 0 to 2 of-7x^3sqrt(x^2+4) ?
The integral from 0 to 2 of-7x^3sqrt(x^2+4) is -7*(64sqrt(2)+64)/(15)