What is the integral from 0 to 1 of (sqrt(x)+x^2) ?

The integral from 0 to 1 of (sqrt(x)+x^2) is 1

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 (sqrt(x)+x^2)

\int_{0}^{1} (x + x^{2}) d x

1

Solution steps

\int_{0}^{1} 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

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

\int_{0}^{1} x d x = \frac{2}{3}

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= \frac{2}{3} + \frac{1}{3}

Simplify

\frac{2}{3} + \frac{1}{3} : 1

= 1

\int_{0.25}^{1.25} e^{- 4 x^{2}} d x

\int_{0}^{2} \frac{1}{2} e^{- \frac{x}{2}} d x

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

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

\int_{0}^{1} x^{3} e^{- x} d x

What is the integral from 0 to 1 of (sqrt(x)+x^2) ?
The integral from 0 to 1 of (sqrt(x)+x^2) is 1