What is the integral from 0 to 5 of (4x-1)^2 ?

The integral from 0 to 5 of (4x-1)^2 is 1715/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 5 of (4x-1)^2

\int_{0}^{5} (4 x - 1)^{2} d x

\frac{1715}{3}

Decimal

571.66666 \dots

Solution steps

\int_{0}^{5} (4 x - 1)^{2} d x

Expand

(4 x - 1)^{2} : 16 x^{2} - 8 x + 1

= \int_{0}^{5} 16 x^{2} - 8 x + 1 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

= \int_{0}^{5} 16 x^{2} d x - \int_{0}^{5} 8 x d x + \int_{0}^{5} 1 d x

\int_{0}^{5} 16 x^{2} d x = \frac{2000}{3}

\int_{0}^{5} 8 x d x = 100

\int_{0}^{5} 1 d x = 5

= \frac{2000}{3} - 100 + 5

Simplify

\frac{2000}{3} - 100 + 5 : \frac{1715}{3}

= \frac{1715}{3}

What is the integral from 0 to 5 of (4x-1)^2 ?
The integral from 0 to 5 of (4x-1)^2 is 1715/3