en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

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

Solution

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

Solution

\frac{5}{3}

+1

Decimal

1.66666 \dots

Solution steps

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

\int_{0}^{1} 4 x d x = 2

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

= 2 - \frac{1}{3}

Simplify

2 - \frac{1}{3} : \frac{5}{3}

= \frac{5}{3}

Graph

Popular Examples

integral from 0 to a of sin^2((3pix)/a)

integral from-3 to 3 of (x+6)sqrt(9-x^2)

integral from 0 to x of e^{-t^5}

integral from-1 to 0 of xarcsin(x)

integral from 1 to 8 of 2/(x^{1/3)}

Frequently Asked Questions (FAQ)

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