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

The integral from 1 to 4 of (x^2+4x+5) is 66

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

66

Solution steps

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

\int_{1}^{4} x^{2} d x = 21

\int_{1}^{4} 4 x d x = 30

\int_{1}^{4} 5 d x = 15

= 21 + 30 + 15

Simplify

= 66

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

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

\int_{0}^{\infty} x \cdot e^{- 3 x} d x

\int_{- 2}^{2} 4 x^{2} d x

\int_{- 3}^{3} (x^{2} - 2)^{2} d x

What is the integral from 1 to 4 of (x^2+4x+5) ?
The integral from 1 to 4 of (x^2+4x+5) is 66