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 1/3

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

\frac{1}{3}

Decimal

0.33333 \dots

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} : \frac{1}{3}

= \frac{1}{3}

\int_{0}^{\infty} 3 e^{- 4 x} d x

\int_{0}^{2} \frac{x ^{4}}{4} d x

\int_{0}^{3} ∣ 5 t - 9 ∣ d t

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

\int_{- 3}^{0} 5 + 9 - x^{2} 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 1/3