What is the integral from 2 to 4 of 2pix(5-x) ?

The integral from 2 to 4 of 2pix(5-x) is (68pi)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 4 of 2pix(5-x)

\int_{2}^{4} 2 π x (5 - x) d x

\frac{68 π}{3}

Decimal Notation

71.20943 \dots

Solution steps

\int_{2}^{4} 2 π x (5 - x) d x

Take the constant out:

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

= 2 π \cdot \int_{2}^{4} x (5 - x) d x

Expand

x (5 - x) : 5 x - x^{2}

= 2 π \cdot \int_{2}^{4} 5 x - 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

= 2 π (\int_{2}^{4} 5 x d x - \int_{2}^{4} x^{2} d x)

\int_{2}^{4} 5 x d x = 30

\int_{2}^{4} x^{2} d x = \frac{56}{3}

= 2 π (30 - \frac{56}{3})

Simplify

2 π (30 - \frac{56}{3}) : \frac{68 π}{3}

= \frac{68 π}{3}

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

\frac{d}{d x} (6 sin (6 x))

- 3

\int \frac{x}{x - 7} d x

\int 5 sin (6 π) t d t

What is the integral from 2 to 4 of 2pix(5-x) ?
The integral from 2 to 4 of 2pix(5-x) is (68pi)/3