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Popular >

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 Notation

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}

Popular Examples

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

\int_{0}^{a} sin^{2} (\frac{3 π x}{a}) d x

integral from 0 to 2 of 0.125(6-x-y)

\int_{0}^{2} 0.125 (6 - x - y) d x

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

\int_{- 3}^{3} (x + 6) 9 - x^{2} d x

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

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

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

\int_{0}^{x} e^{- t^{5}} d t

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