What is the integral from 0 to 1 of pi(x-x^{10}) ?

The integral from 0 to 1 of pi(x-x^{10}) is pi 9/22

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 pi(x-x^{10})

\int_{0}^{1} π (x - x^{10}) d x

π \frac{9}{22}

Decimal Notation

1.28519 \dots

Solution steps

\int_{0}^{1} π (x - x^{10}) d x

Take the constant out:

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

= π \cdot \int_{0}^{1} x - x^{10} 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

= π (\int_{0}^{1} x d x - \int_{0}^{1} x^{10} d x)

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

\int_{0}^{1} x^{10} d x = \frac{1}{11}

= π (\frac{1}{2} - \frac{1}{11})

Join

\frac{1}{2} - \frac{1}{11} : \frac{9}{22}

= π \frac{9}{22}

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

4 x^{3} - 12 x^{2}

\frac{d}{d x} (e^{7 x - 4})

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

\frac{d y}{d x} = 2 (x + 1) - y

What is the integral from 0 to 1 of pi(x-x^{10}) ?
The integral from 0 to 1 of pi(x-x^{10}) is pi 9/22