What is the integral from 1 to 6 of (x^2-4x+5) ?

The integral from 1 to 6 of (x^2-4x+5) is 80/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 6 of (x^2-4x+5)

\int_{1}^{6} (x^{2} - 4 x + 5) d x

\frac{80}{3}

Decimal Notation

26.66666 \dots

Solution steps

\int_{1}^{6} x^{2} - 4 x + 5 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_{1}^{6} x^{2} d x - \int_{1}^{6} 4 x d x + \int_{1}^{6} 5 d x

\int_{1}^{6} x^{2} d x = \frac{215}{3}

\int_{1}^{6} 4 x d x = 70

\int_{1}^{6} 5 d x = 25

= \frac{215}{3} - 70 + 25

Simplify

\frac{215}{3} - 70 + 25 : \frac{80}{3}

= \frac{80}{3}

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

\int_{0}^{\frac{π}{10}} cos^{2} (5 θ) d θ

\int_{1}^{3} 3 t^{2} - 12 t + 9 d t

\int_{0}^{2} 25 - 3 x d x

\int_{1}^{5} 5 x + 4 d x

What is the integral from 1 to 6 of (x^2-4x+5) ?
The integral from 1 to 6 of (x^2-4x+5) is 80/3